That's odd. Do you use the app assignment feature to assign apps to particular spaces? Or you just start an each app on the space you want it on?
I guess the latter. but either way I'm not sure why your windows are moving.
One thing that can happen is that if you are clicking on the title bar of a window when you change space then the window will move also. But if you aren't doing this, then I don't see why the window would move.
Can you think of any other clues - anything else that might trigger the issue?