I imported artwork designed in Illustrator using the correct layer structure and when inside Character Animator the mouth moves continuously on its own, even while my mouth is closed. Any idea why it might be doing this?
Lipsync is the normal way the mouth is controlled. Lipsync uses two different inputs for mouth positions - audio and webcam. Surprised and smile use the webcam to work out if you are surprised or smiling - not audio. The rest use audio analysis to guess the “viseme” (Ah, E, etc sounds). If you record a take, you can see the viseme names in the scene timeline panel.
I am wondering if you are seeing the visual (Smile/Surprised) visemes or the audio visemes. If only the audio visemes, then do you have music or similar feeding into the system? Or white noise? It might be picking up on that.
If its neither of the above, then it could be something like a Cycle layers behavior running through them all. (Strange, but possible.)
So some more information would be helpful - e.g. screenshot of the rigging, and record a take and see what visemes are appearing in the timeline.