Your deformation order is out of sync on the mesh
You are calculating the wrap deform before you are calculating the skinCluster! Right click your object, choose Inputs and go to All Inputs… you will see your wrap deformer and your skinCluster in the window, move your wrap deformer below the skinCluster (middle mouse button, click & hold, drag below skinCluster).
Basically it’s just inheriting transforms down the hierarchy type deal.
Now just out of curiosity why are you skinning the wrap deformer to the bones? Would usually just want to skin the base mesh to your joints and then wrap deform the other mesh overtop and have that driven by the base mesh…