This is probably just a bad Parenting method for some of the Facial Rig elements.
On Facial Rigging, usually, it’s beneficial to have a same, single Bone of reference to Parent (on different methods) all sort of Rig features.
This Bone of reference is usually the Head Bone. Sometimes, it doesn’t matter if it’s the DEF Head Bone of the Deform Rig, or if it’s the CTL Head Bone of the Control Rig; but it may matter if one starts Parenting on both of them randomly; it’s better to focus on a single one; I believe that the Head Bone (if available) from the Control Rig is a better reference of Parenting for all the Facial Rig features.
The method of Parenting is very relevant also.
If you’ve got a Theeth Mesh Object that is supposed to be rigid, it may receive a Bone Parenting method (Set Parent To Bone), Targeting the Head Bone of the Armature Object; don’t use “Relative” Bone Parenting, unless you know exactly what this is about (don’t ask me, I could never figure it out entirely). Bone Parenting doesn’t require Deform Bones, nor Weight Paint.
However, if the Theeth Mesh Object is Deformable, or you prefer this method anyways, you’d need first to Add Deform Bones, Position them properly in relation to the Mesh Object(s), and then use Set Parent To Armature Deform (With Empty Weights, to avoid issues), and then solve the Weight Paint ‘manually’ (use Set Weight [Shift+K] set to 1.000 on all the Mesh, use Paint Mask Option to gain time and be exact). Of course, these Deform Bones must be Parented Offset to… the Head Bone.
There exist plenty of other special cases of Parenting for Facial Rig features (and LOTS of things that can go incredibly wrong: a single mistake can cause horrid wreak havoc, which, depending on the complexity of the Rig, may be even difficult to track back and solve without a backup file). For the majority of cases, make sure all Objects’ Origins are correct (usually, all matching on the same spot, for example, the World Origin; naturally, there exist exceptions), and that all the Objects’ Transforms are Reset and Applied, and everything is matching accordingly.
Hope that helps;
Pxy-Gnomes.