How do you know when you villager has mastered the 4 plants. Or do they have to master healing?

You will get a message when that puzzle is oomplete, and it will be displayed on your Puzzles screen.

The game will tell you when this happens -- you'll know.

Keep trying with the plants if you haven't gotten the message about getting all 4 -- the villager may fail a few times before mastering that particular plant.

And it only happens once, afaik.