When I play Native Village, I can only tell what happened by reading the log. I can't see the card that entered the mat, or the contents of the mat.
If you hover your mouse pointer over your player name, you can see the mat's contents on the right side (over the log). Clicking your player name keeps the mat area open (so you can scroll there if required) until something new is written into the log.
It's "mystery meat navigation", information hidden unless you mouse over an unannounced spot. Not a good design for a UI.
I agree, it usually isn't. Maybe a small icon looking remotely like the tavern mat / Island mat / Native Village mat respectively like a duration card would help. Of course, some users would then immediately complain that the screen has become even more cluttered...
I've had a problem with this as well. I'll try mousing over, thanks for the hint. I still think it should be visible without having to look for it.