Took a look in v7.32 and was unable to duplicate your issue. Every overlay, whether text or video, followed the timeline during play and export.
Spotted two incorrect overlays, at about 5:56 and 17:03, where the desired video was overridden by a higher track.
Back up the project. Then go to Control Panel|Programs and Features and right-click the Videopad item. Uninstall, including data files. Then install the current release version.
Report results here.