Okay, as mentioned prior, the reticle will move in the opposite direction that you want the POI to move. The easiest way to describe this is to exagerate everything. If you want the POI (point of impact) to move upward, and lets say you have no adjustment in the scope (just for ease of explanation), you would need to shim under the rear base. Lets say you lift it an inch... Again, exagerated... That scope would be pointing at the end of the barrel. This would force you to lift the barrel upward to aim at the target through the scope. Same effect with moving the reticle assembly...
As for loosening the screws on the turrets and retightening with a POI shift... There is absolutely no way this could happen if the screws are completely loose. After loosening all the screws (three on standard turrets, one on the M1), you should be able to free-spin that turret (or take it off). There is no way that taking that off or spinning it could change anything... Make sure all the screws are loose when you turn them.
Hope this helps, let me know if you have any more questions...
DFA