Aidan figured out what was happening; if you select the second object it will update the anchor and set to that anchor. The text input for the anchor is only updating the input and not the value used by the behaviour, but selecting the anchor manually updates both.
@Deeeds If the object’s old image has the exact same resolution as the previous image, you won’t have this problem. Just as long as whatever is in the image is in the same place in both images, if that makes sense.