When you start moving the table does the dial move a few divisions almost immediately, then stabilize and move back about the same amount after you stop moving?
Your table may be moving due to the formation of a dynamic oil film during motion which squeezes out when the table is stationary. I have seen this on old lathes with sleeve bearings on the spindle. When the spindle is turned it lifts slightly due to the oil film that is dragged between the spindle and bearing due to the motion, and then it settles down when it is stationary. Depending on the viscosity of the oil, the running clearance and the rate of rotation the movement can be quite large.
An open mind is a virtue...so long as all the common sense has not leaked out.