Constrained object´s texture maps are drifting

I have a simple setup of a book constrained transformation to the characters hand bone. But now the texture maps are drifting! How can I fix this?

Appears to be that this was some kind of texture variation hack by the creator of this excellent Bookworm Experiment UE scene.

See here:

I managed to hide this effect by altering the materials layer 1 contrast
& brightness values.

But still it is there. How can I make the colors stay stable on animated books?