/tmp directory, it is cleared on reboot
If it's tmpfs (valid for some newer distros), then yes. Otherwise it's not generally cleaned up on reboot or shut down. Old files in it could be cleaned up by a cron task but I last saw that over a decade ago.
what happens to the living host whenever the /tmp folder is flooded (put to the max storage capacity)
Nothing much, most Linux utilities/services don't actively write to /tmp. If they do, it's solely application dependent.
does Linux have some sort of fail safe to this, or will it, until reboot, leave the files there?
No failsafe that I'm aware of. It's your responsibility as a user.