Your puppet structure seems to be fine from what I can see. For the main "Mouth" group, did you check "hide siblings" (might not be the exact wording, but it's the 1st or 2nd checkbox within the "Triggers (obsolete)" panel on the lower right hand side.
Alright, this is weird.
I have to do a combination of swap sets + the obsolete triggers to get it all to work correctly.
I hope that Adobe can fix this weird bug. I do not see the point of creating this new way of functioning if it does not work
Thank you for answering my question
It looks like this might be happening because your neutral mouth is in a different group than the alt mouth. When you set up the swap set (which looks correct) it is conflicting because it is hiding the siblings in the alt mouth group (smile, and mouth sad) but neutral is not in that group. IDK your reasons for having it in a separate group, but try putting all the mouths in the same group, and see if it works better.
You don't seem to be using the lip synch mouth shapes to do speech correct?