Ideally, a used computer store selling used computers "should" erase the drive using a 2 pass and higher and re-install a fresh OSX on your mini. The admin password should be set up by the store, not by the former owner. Which meant that there could be private data in that Mini which violates the Data Prohibitive Directive of the EU and the machine shouldn't be sold like that. I work in a computer recycling business not in the UK, but sells used Macs. We always delete the drive using the 7 pass method and then put a fresh OSX install with a store admin password which we give to our customers to transfer over their credentials to the machine.
Anyhow, it's important to get the admin password, because you want to know whether the former owner deauthorized this Mini in iTunes or it has a firmware password protection in place. The 2008-2009 are easier to over ride, but the 2011-2014 are slightly more difficult and the 2018 with the T2 chip is virtually impossible to over ride. The implication is that, you would not be able to install the OS through Internet Recovery as it could put you in an error and can not factory reset the Mini if the user place some sort of password protection on it. The T2 equipped Mini with its security chip is virtually impossible to break and reset with any sort of admin password. Don't buy a T2 equipped machine without knowing that it has been de-authorized and without any password protection enabled.
