This is an order of execution problem which crops up from time to time. You have to understand that there are two factors that affect the order in which things are executed by Cinema:
1. The stacking order of objects in the Object Manager; and
2. The priorities assigned to classes of objects and to tags (which can be changed in the tags' Basic tab.
In this case I think you can fix the problem by moving the spline wrap deformer below the dynamic spline in the Object Manager. I'm not talking about heirarchy, but it just has to be lower than the spline in the object list. That's because objects at the top of the list are evaluated before objects lower in the list. Since the spline wrap deformer has to evaluate the position of the spline, the spline movement has to happen first.