Did I have the opportunity to choose sides? Or why was everyone but some assassins green in the fight?

(I'm talking about the two big, huge, giant things.)

Do you really expect to be able to kill a frost giant as a level 1 character?
They are green so you can't accidentally attack those as they are supposed to keep Jamandi busy so you actually have a reason to kill all the sidekicks as Jamandi would just drop all of them down alone.

So to anwser your question : it's a feature. The "bosses" from both camps (Jamandi and the Giant) are fighting each other while the sidekicks (the assassins and you, sorry you're still level 1) are fighting apart.

Amari claims endlessly that she killed a bunch of frost giants before the adventure started.