I believe that spring is the cam spring. When the movement is removed from the case the spring end can then clear the movement rim releasing the spring tension on the setting cam which in turn disengages the setting function. It’s possible that the clutch and setting components are just sluggish and not moving into position when the movement is cased or that the shipper spring is not positioned correctly or something is out of place resulting in some dragging somewhere. If everything responds well when manually working the pieces back and forth then a good cleaning will often take care of this problem.
Please keep us posted and let me know if I’m missing something here.