This might be due to the fact that when you rotate an overlay with the anchor point 0.5 0.5 (center) it always shifts positions. This is because the default anchor point is 0 0 (left bottom) and when you tell it to change anchor points, it repositions. Hope that makes sense? 
So in order for it too look normally, you have to position the overlay again after the rotation and change its origianl coordinates.
Example:
INT. BACKGROUND with OVERLAY to 1.234 123 123
&overlay OVERLAY rotates 360 anchor point 0.5 0.5 in 1
#You can click on the "Line by line" mode on the previewer so the script
#stops here. Now reposition the overlay and change the original coordinates
Here’s a tutorial on animating overlays, it also explains rotation and the repositioning:
Good luck! 