Hi MMB-
The exact process is outlined in this guide, along with a video tutorial.
Generally speaking, the behavior you’re describing- that WordPress prompts you to re-install- happens when the site doesn’t find the WordPress database tables. I can think of two different possibilities that might cause that.
1. Your staging sub-domain has a different database prefix than your production site, and you’re using the restore option instead of the transfer option. If this is the case, make sure you’re using the transfers tab to perform the migration.
2. The backup archive that you’re transferring has an empty database export due to an error in the backup process. If this is the case, we may be able to spot some errors from the archive log on your production site. Navigate to Total Upkeep > Tools > Logs and find the archive-XXXX-.log file that corresponds to the timestamp of that backup. Copy that text, and reply back here, and we can take a look for you.