if jenkins is already idle (in that no jobs are running), and the "Wait until Jenkins/Hudson is idle to perform a backup" option is selected, jenkins will never enter quiet state.
In waitUntilIdleAndSwitchToQuietMode(): https://github.com/jenkinsci/thin-backup-plugin/blob/master/src/main/java/org/jvnet/hudson/plugins/thinbackup/utils/Utils.java#L101 it only actually switches to quiet mode if there are still jobs running by the time the timeout time has passed. this means that if jenkins is idle when the backup is triggered, jenkins will not enter quiet mode, the backup can start, and then jenkins is able to freely start any other job while the backup is in the middle of running
Note there's also a potential problem if any jobs are blocking jobs. If quiet mode is enabled while a blocking job is running, then the downstream will never start (never leave the queue) and then you'll have total deadlock where neither the backup nor build can continue