I had the same problem and I think I figured it out. The issue is that the face mesh is influenced by both spine 6 and 5 bones - with spine 5 influencing it only ever so slightly. So what I did:
went to weight paint of the body mesh and painted eye area weight of spine 6 vertex group to 1
then selected spine 5 vertex group and painted that area to weight 0
now it all sits on top of each other like glued no matter how extreme the pose is. Hope this helps whoever is in this spot… and I assume it will also be fixe din weight paint lesson I havent watched yet