I think I found the problem. I therefore document it here for somebody who may encounter the same problem in future.
I believe it is caused by the combination of the following factors:
Rigging the model as a set of separate objects to the same armature, and
Having IK constraints higher up in the rig
I have an IK constraint on the forearm, with the target at the wrist. I also added a pole target to control the elbow’s angle. Activating the IK causes a slight movement in the rig. The mesh is also very sensitive to the pole angle.
It seems as if the hand (as a separate object), although being modified by the rig, did not seem to “be aware” of the IK constraint above it.
I now merely joined the hand mesh with the forearm mesh - and the problem seems resolved. (The meshes are still not linked, only joined, i.e. I did not connect any of their vertices)
Hi, this is a little off-topic, but it’s better to put the Subsurf modifier underneath the Armature modifier. In your case the armature deformation happens after the subsurf, which will make things slow and give ugly deformation