I'll have to look closer next time I change strings, it seems like there's nothing there holding the saddles in place once I take the strings off and they can just slide back and forth until there's tension on the string again. Thanks for the link.
Check the screw on the bottom right of each saddle. It should be tight. There’s no reason for the saddle to move if it is, and every reason for it to do so if it’s loose.