Can't get my puppet's head to tilt

In the "body" group you have a hidden "Lines" layer that's doesn't overlap anything else, so the default Mesh Shape of Auto will switch to a rectangular mesh to encompass all of the pieces. (It looks at the hidden layer and tries to include it in the mesh in case you might trigger it on.)

As for the head tilt, after removing the Lines layer, try increasing Head Tilt Strength.

I'm not an expert but a beginner. So here's a suggestion in that category. Make sure you don't have little tiny parts left around the character. It will throw everything off. I always do a sweep around the "blank" spaces in Illustrator when I'm importing assets to CA.

Nice artwork!

I think the problem is you have the "head" layer as NOT an independent group, and the children "frontal", "left profile" etc as independent groups. The "head" tag (used by the face tracking" is therefore associated with the main body, not the different profiles. The main body then moves with the head, but the actual head profiles are independent, so are not affected. I removed the "head" tag manually from the "head" layer, then added the "head" tag to each of "frontal", "left profile", "left quartile" etc and it started working.

Not sure if this is the correct approach - I have not used head turners yet - but it seemed to work. (I don't know if a better solution is to make the "head" layer independent instead for example).

You may also want to reduce the "head position strength" to keep the head closer to the rest of the body (it floats away a bit when I was playing with it).