Added mouth, automatic weights, face pops out, no!

So I have my human baby rigged. Great.

I added back its mouth cavity mesh. Great.

I de-parented the bones and kept transformation, then parented them again with automatic weights. Then, it’s face/muzzle pops out just a bit and I didn’t want that to happen!! Help!

Basically I added mesh in its head, and want to parent the mesh with the bones to rig it. But I don’t want its whole mouth/head to morph and change shape/pop out a tad.

Any clue?