This is the result of a bug in version prior to V5.0.2. When a part is moved to the bottom side of the board in older versions it mirrored the part, but also displaced it from the exact mirrored position. The user would then account for the error by moving the reference designator into the expected position. Now when you open the layout in the latest release PCB123 is accounting for the bug and moving the reference designator where the software expected it. This results in bottom side reference designators not being where you last left them. I appologize for the inconvenience but this is the result of a bug fix.
Please contact customer support if you have any questions.