How to start a VNC session on mac-mini to remotely log in, not screen sharing?

On a mac mini, how can I log on with VNC remotely from a Linux workstation, without affecting the screen on the mac mini? I mean that I don't see the screen on the mac mini, and they don't see anything on their screen that I am connected or see my VNC "virtual" screen. I have an account on the mac mini and can log on locally. But need to log in remotely, while someone else is logged into the mac mini (or will log in) without interfering with each other.