I thought the insertion of a new activity has only local impact. After reading some other posts on the forum, there were severel conversations where it was stated that the insertion has global effect.
I was trying to understand this through the constraints of the jsprit core. For example if a new activity is inserted, the activies after that may be shifted, thus there is a chance that the activites after the new one, will be out of their timewindows. But after looking at the TimeWindow constraint in VehicleDependentTimeWindowConstraints, I did not see any code that will deny the insertion in case when shifting happens.