OP:
Some thoughts...
If you want to "revert" a Mini back from Catalina to Mojave, I recommend that you DO NOT try to do so from a TM backup.
Instead, create a BOOTABLE CLONED backup using either CarbonCopyCloner or SuperDuper. It will make the process easier.
When you get the new Mini (assuming it has Catalina on it), you will need to do a few things:
- First, create a basic account. You DO NOT need to "migrate" anything to this account. But you CANNOT disable startup security until you do so. (because you must enter an administrative password to open startup security and you can't do this without an account)
- Boot to the recovery partition
- Next, go to startup security and DISABLE all "features". You want to choose "no security" and "allow booting from external media".
- Finally, open terminal and disable SIP with this command:
sudo spctl --master-disable
Now you can boot from an external source, ERASE the internal drive, and put a copy of Mojave onto it.