If the computer has seen any Mac OS X upgrade from Lion 10.7.2 or newer
the EFI Firmware Update 1.5 should have been installed automatically...
But if not, and nothing newer had been installed, then this EFI Update may
be important and without it, there may be issues as suggested in following:
• Mac mini (Mid 2010) EFI Firmware Update 1.5
//support.apple.com/kb/DL1479?locale=en_US
This article lists firmware updates available as standalone installers for Intel-based
Mac computers. ... Mac mini (Mid 2010) Macmini4,1: MM41.0042.B03 ...
//support.apple.com/en-us/HT201518
Sometimes the original software may not be installed if the media is damaged
or the optical drive is dusty or failed. On rare occasion, an upgrade to much
later OS X may change the boot firmware. That may render Mac unable to run
from old original software's installer. (A clone of original software may boot.)
A 'copy of an installer' may not be the correct software to do what you need.
'Diskmaker X' is like the Lion Disk Maker, if you find & used that, it may work...
http://diskmakerx.com/ there are older versions
Usually the macOS Recovery from Apple network server can be used if you
have suitable OS X in Purchases History in Apple ID, to re-download + install.
How did you re-format the hard disk drive after erasure? ~ Same issue arises
if one were to replace an old hard drive with new one. Use Internet Recovery
in that booted version of macOS Utilities to prepare the drive for new install.
If the firmware were upgraded ~ so the Recovery could be used.
Sometimes you could use a second Mac to help restore the hard drive and
install a replacement system in one that has issues, or needs upgrades. The
target disk mode (if suitable ports exist in both, or if adapters can be used)
is one way to try and work around some issues.
Where did you see the existing Firmware version wasn't correct for this Mac Mini?
If there is another corruption or logic board damage, that may also cause an issue.
• Find an Apple Authorized Service Provider
An Apple Authorized Service Provider may be able to check and install an EFI Update.
And the early OS X. -- Or test and tell you why it does or does not work as expected.
I've only had two Mac Mini computers, both here & working now. Late 2005 and Late
2012. And both are the last of their respective build models. Never had issues with my
300+ other Macs; some few requiring it, I upgraded firmware & other system software.
Perhaps someone may offer a short solution?
Good luck & happy trails! 🙂