I tried to follow the OkaySamurai tutorial on creating a swap set to trigger a swap between a happy mouth and a sad mouth, but what i get instead = happy (default) mouth, lip lync no problem. Trigger the sad mouth, it shows the whole stack of mouth shapes with no lip sync happening. Both mouth sets are tagged as mouths and as far as I can tell, everything is set up the same as in OkaySamurai's video.
Here's a screenshot of the puppet in rig mode. You can see the groups labelled Talking, Mouth, and AltMouth like in the video, and the AltMouth is highlighted so you can see it's tagged as a mouth...
I always forget when needed, but if you look at the lipsync behavior in rigging mode and expand it, i bet it found one mouth layer, not two. E.g. 'altmouth' won't get auto tagged (unless you put a space in it). So it may be as simple as renaming to "alt mouth". But lipsync looks for the mouth layer first, then visemes under that. If it did not recognize the mouth layer, you will get what you see. (I don't think you need to add a second mouth behavior when i tried last time - there was a post in the last month or two where i tried a few things - forgot already sorry!).
In the tags panel i suggest clicking the "a" button to see layer names and compare between the two mouth and altmouth layers to look for differences. I trust it more.