If it's a separate partition, it should be unmounted between backups. If it's left mounted and a hacker gets in, it makes it easier for them to damage the backup files as well, or if someone does rm -Rf * from the / directory in shell, you'll wish backup was unmounted.
That's true, but if a script goes haywire, or a user makes a serious mistake, unmounted is safer. Safest is off server backup, but for on server backup, there are minor advantages to unmounting.
I don't know if the mount/unmount was designed with Linux in mind, but on FBSD , the feature doesn't work properly. When the drive is unmounted by cPanel, it is unable to mount it back in!