I believe that the issue is with iOS and not the specific app. What's happening is that iOS is still relating files saved from Rush to the application.
The fix that worked for me was to back the phone up to a pc. For some reason a pc backup re-relates the files so they are associated with your Photos or Files space and not the app anymore.
It's been a while since I did it, but I recall that the files were already being backed up to iCloud through the Photos and Files applications, so fixing the relation issue didn't increase the storage usage of Photos or Files, since the data was essentially being backed up twice.