In order to provide the best possible spreading, the roller should run at exactly web speed so as to leave the most traction possible for spreading. Once the roller slips, traction for spreading is lost.
The drive must be speed matched for all steady speeds. This is easy to do. The drive must also be speed matched during acceleration and deceleration. Various means of inertia compensation can be applied to help the spreader roller track speed during speed changes. I suggest the drive be used with an encoder, rather than running it encoderless. The picture of the paper roll with rings shows defects definitely associated with improperly tuned spreader roller drives.
Droop may also be needed to assist with speed tacking during speed changes. Friction and windage compensation may also be needed as the friction in a spreader roller is significant.