I had the exact same problem, and I was frustrated because I looked everywhere for the answer. I even read through all the documentation, but they leave out an important point. When you create the sub folders in PS with three quarters and profiles, and then bring that puppet into Character Animator, you need to add a Face Behavior to each folder in ChA. So click on the puppet tab, then select all the folders you want to apply the Behavior to, and then on the right hand side click "+" by Behaviors and select Face. Then you will have independent controls over the face behaviors and your puppet should work properly after that.
Brilliant. That did the trick. Thanks Dave!
Glad I could be of help.
We're aware of how annoying this is. So the forthcoming Preview 4 will not require it -- the Face & Lip Sync behavior at the root of the puppet will control faces/mouths in all views. (Though you'll still be able to apply the extra instances to get individual controls.)