Inconsistent results when aligning layers

I need some advice regarding aligning layers, for example suppose I have a circle that’s off-center somewhere and I want to add an element to be on that circle, and it’s dragged as close as possible by eye. When I try to align the new element on the circle, I get inconsistent results. Sometimes the circle will shift to match the new image, sometimes the new image shifts over the circle as intended, and sometimes both shift to meet somewhere in the middle. I’ve tried locking the circle but it still will move. I’ve tried changing relative position (circle over/under the new image), but no luck.

What is the best way to do this? The only way I can think of to guarantee this is to center the stack of images in the center of the face (255,255) align the images with the “center” tool, and then move the stack back to it’s desired location. This seems somewhat inefficient.

What am I doing wrong?

I am not sure why you cant write the same x coordinate into placement of each element directly, but that would give the most precise result.
I played with it and the results seemed pretty consistent to me. When two components are selected, they together have new common area size and they are both aligned to the edge or center of this common area, depending which button you press. Happen the new element to fit into the area of your circle before the alignment, then the circle wont move. Happen the circle fit into area of that new element, then the element wont move and the circle will shift to align to it. Do they overlap partially, then they will shift both to center of the common envelope.