I appreciate this response, however, we have been backing up the same way for years now. 

We do choose "Local Backup". It gets backed up to his local Drop Box folder, and then the Drop Box folder syncs up on my end. (And then I restore on my end) It has ALWAYS been the normal back up file. As I said, it is only the last 2 times that it has instead created this "temp" back up file instead. 

And I also use the exact same method to back up, and it creates the normal back up file, like always, and he is able to restore from mine, just fine, like always.