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I like the combat in this game. I like that it has rules and doesn't rely on RNG. However, something isn't right with overwatch. The only thing in the manual about overwatch is:
Use Overwatch when you’re defending a position or if you have a spare Action Point. This ensures that if an enemy moves within range that you can preemptively strike.
It doesn't seem to work that way in my experience. Most of the time you never preemptively strike and either get shot by an enemy in your overwatch or they run through your overwatch and shoot you.

Sometimes it works, but so far it seems to completely fail more often than it succeeds. In the early mission (playing as CIA) where you have to fight your way out of the assault on your base and destroy evidence, it worked and failed at the same time. I had a road covered by two agents in overwatch while two went in the building and two moving to cover our back. An enemy soldier ran out of a building across the street and got mowed down by my agents. Two more soldiers were in that building (which I didn't know at the time) and did the smart thing and stayed put, going into overwatch themselves. I discovered them a few turns later with my Navy Seal agent using the heart beat sensor. They stayed there for a long time, apparently afraid to come out after watching their buddy get obliterated.

Toward the end of that mission while making a run for the evac, I thought I had taken out all of the enemy soldiers and was rushing to the evac before an airstrike and reinforcements arrived. I was wrong, and alone soldier was inside a building across the map and shot down one of my agents as we ran across the open toward the evac zone. I saw where he was when he fired, but none of my agents could see him when it was my turn. I moved my agents into cover and put them into overwatch covering the direction he fired from. I thought that if I can't see him, he can't see me, but on the enemy turn, he took a shot at my agents again. My agents in overwatch didn't react. I moved farther back, staying behind cover and keeping overwatch in the direction he was hiding. I thought for sure he would have to move closer to get a shot and I'd get him with overwatch, but nope, he stayed put and was still able to shoot my agents from his position despite my agents not being able to see him. I was able to stabilize my downed agent and reach the evac, but took fire from this guy every turn. I only saw him when it was the enemy turn when he shot, but not when it was my turn.

In another story mission where you're forced into combat, I had an enemy run right through my overwatch and grenade two of my agents. I saw her in the window above the building before we ran in there to take cover from an incoming air strike. I've attached a screen shots of the turn after. In the first screen shot, the enemy was in the window directly above the door. The second screen shot shows the inside of the room my agents were in and where the enemy moved to. I expected the enemy to come down the stairs, so I had agents Deadpan and Durand on overwatch covering the stairs and the open door behind it. Agent Canasta was on overwatch covering the area out the door looking to the top of the screen in case enemies came out from the two doors up there. On the enemy turn, the enemy upstairs jumps out the window, runs in the door into that corner and throws a grenade hitting Deadpan and Durand without triggering Agent Canasta's overwatch..

Since then I've been completing most missions without combat. When I have gotten into combat, it's usually because I got careless going to the evac and got spotted, and then I just run for it rather than stand and fight.

I had two missions last night where I got into combat and I had to defend while waiting for the evac. Overwatch worked once, and failed the rest of the time. In the situation where it worked, my agent could see an enemy though a window above. They weren't in the half cover squares in front of the window, but one square behind it and in full cover behind something else. I couldn't get a decent shot, so I used overwatch on the window. On the enemy turn, that enemy moved to the window and my agent on overwatch lit them up, killing them.

The first time where it didn't work I got careless after completing the objective and sent a don-disguised agent through a restricted area which alerted the enemy. Evac had been called, so we just had to wait and defend ourselves. It was a similar situation. to the first, my agent was outside behind full cover. I knew there was an enemy agent in a room on the 2nd floor because during infiltration I saw them in there. My agent couldn't see them, so I put them on overwatch on a window looking into that room. I was a 2-square wide window and I was only able to get the two squares just inside the window to highlight. On the enemy turn, two enemy guards somehow made it to that window without triggering my agent's overwatch and shot my agent up.

Overwatch failed again on this same mission, the very next turn. I dispatched the two enemies in the window with a grenade. A 3rd enemy showed up on the corner of the building and fired at a different agent on the turn when the agents moved to the window. From where my agent was, the full cover of the enemy plus their full awareness meant I didn't have a good shot at them, so I moved my agent to what I thought was a better position. It was full cover and looked like I would have a direct shot at them, but the enemy was still considered in full cover, even though the line of sight looked like I should have a direct shot on them. I put my agent on overwatch covering that enemy on the corner thinking that if they shot at one of my agents, my agent on overwatch would react and shoot them first.. The enemy turn comes and that enemy on the corner opens fire at my agent on overwatch and my agent doesn't react.

I'm guessing that since the square the enemy was standing on was behind cover and the overwatch zone didn't highlight it is the reason my agent didn't react. When the enemy fires, the animation shows them stepping out of the cover into an adjacent square which was covered, and I assumed my agent on overwatch would be able to hit them when they stepped out to take a shot.

There have been other times when overwatch failed to work, such as having overwatch on a door I suspected an enemy to come through, but instead they were moved into the cover beside it, which is fine, but then they are able to step out into the open and fire at me without my agent in overwatch getting to "preemptively strike," which is not fine.

This is not the way I expected overwatch to work. Overwatch should give you the advantage to act first if an enemy in the covered zone moves OR shoots. Overwatch, as in the name implies, means you are watching over an enemy or area, waiting for them to make a move and react when they do.

I think there are definite bugs with overwatch, like enemies being able to move through the overwatch zone, but other than that, the "rules" for overwatch need changing. As I said above, overwatch should work not only for enemies moving through your overwatch, but for enemies that shoot. They can't shoot from cover, they have to step out of the cover to fire, and then the overwatching unit should get to act first.

Overwatch shouldn't be overpowered either, otherwise the player or the AI will just spam it. Suppression should be a counter to overwatch. It could be a paper scissors rock kind of thing, where overwatch beats fire and movement, and suppression beats overwatch. For example, an agent in cover that is not on overwatch takes a burst of full-auto fire and becomes suppressed. That agent then can't use overwatch to gain an advantage on the next turn. If you or an enemy is in overwatch watching in one direction and you take full-auto fire from another direction, it should break overwatch for that turn. This would add some extra tactics to the combat in the game. You could also add an awareness cost to overwatch, perhaps costing more awareness to cover a wider/longer area.
I ran into a similiar issues. All were only observed with non-player units moving.

1) Non-player unit starts turn in an overwatch zone and moves. Player unit does not react.

2) Non-player unit crosses, ie. enters and leaves, an overwatch zone. Player unit does not react.

3) Non-player units ends turn in overwatch zone. Player unit does not react.

I was careful to observe if overwatch was disabled by non-player units by special abilities, but apparently it wasn't.

Steps to reproduce:
A good testing ground is the early ambush scenario in the KGB storyline, where three KGB (player units) have the table turned on them and are ambushed while tailing some GRU operatives.

You start in the office on the second floor. Move outside, over the construction platfrom, to the back of the map. Then move towards the left hand building corner leading to the evacuation area and the lorry there. This takes a turn or two.

Once there, set up an overwatch zone towards the door and the crates next to the door. There, behind the crates, a police man is waiting. Also, usually two soldiers and an agent come through the door on the same turn or one turn later. Often the police man just fires his gun and does not trigger overwatch. Most often one, rarely two soldiers, come out and hide behind the cable roll, the agent usually seeks cover in front of the lorry. All of them usually don't trigger overwatch, despite entering or crossing overwatch zones.

Next, if enough player units survive, move further towards the second lorry, near the evac zone. Set up overwatch zones again, this time covering the door, the soldier and the agent. Those non-player units always move, sometimes staying in the overwatch zone, sometimes leaving it. On both occasions they are not triggering overwatch.

Have fun.