Hello,
The wire deformer is one of the most powerful Maya deformers. First of all, because it is very fast to evaluate and now In Maya 2019, it is going to be even faster.
The deformer needs some help though when we try to make it rotate an object.
In order to properly transform an object which is deformed by the wire deformer,
we have to transform The object, the wire deformer curve, and the wire-base curve together.
(this last one is created with the deformer and it is essential to calculate the deformation.)
In your case, you probably have the deforming curve parented to your animation control
while the base-curve and the geometry are out of that transformation.
Group the geometry, the deforming curve, and the base curve together and then let
this group being constrained by (or parented to) the animation control.
I post you 3 examples.
1. basic: just the eyebrow following the head transformations (maybe like in your scene)
2. intermediate: the wire has clusters to shape the eyebrows (the clusters need to be relative and in the same group of curve, geo and base-curve)
3. advanced: the clusters have controls and they follow the face deformation.
(if clusters are constrained by controls, the clusters will be out of the transformed group and the controls will be in)
the basic concept is that geo, curve and base curve need to move together.
Cheers
D