Imported a character rig from a SWF, made into library template, now mouth position is inconsistent

I did the process of taking a character previously made in Flash and importing it into Animate 3, followed up with sticking the whole thing to a peg and saving it as a template file in my Animate library. However, while things work fine when I test the original file with the SWF import, I’ve come across a strange issue regarding the mouth for the template file.

Normally, it should be positioned like this:

However, when I drag the whole character across the scene, the mouth gradually shifts independently to such positions as this:

Also, when I try to switch between the various mouth shapes I made using the template version, this is the typical position I get when the previous shape is perfectly centered:

Is there a known way to fix this issue?

It’s not possible to answer this without seeing the project but it probably
has something to do with how the character structure was implemented in

You should contact support to have a look at your project to determine
how best to correct the mouth. Normally all face features (or rather their
pegs) should be “children” attached to the peg of the head/face so that
they move together as one unit.