Where can I find the treasure in the Alvaron Place of Execution that I got a map for? I checked the cache next to the area where some people got hung. was that it? If not, where can I find it?

I couldn't find any stumps in the Execution area.

Generally, you can tell you found the correct cache because its key (or Treasure map in this case) disappears from your inventory. The treasure of Baron Mansfeld in the Alvaron Place of Execution area lies under a tree stump, in fact. See the attached screenshot to find the correct place.