I have 2 adept healers that all they've done is study 2 of the herbs/flowers. Does a pop up show when they've mastered one of them? Am I just being impatient?

ummm..you can drag them over to all of the different ones on the Island yourself. Mine always study the red or the purple rose.
If you are referring to when it says your villagers have mastered this herb, usually after a moment or two of studying the plant, but you have to watch the bottom of the screen, because it does not stay long.

Thanks, I didn't realize that you just waited until the game said improved in healing, then move on to the next plant