Well, Apple's page states (
https://support.apple.com/kb/sp659?locale=en_US) that this Mac mini is capable of "Support for up to two displays at 2560 by 1600 pixels, both at millions of colors". So I'm like, WTF.
That statement on Apple's page is true but it is ambiguous, it says "up to", with a catch.
Here on this site it lists more:
https://everymac.com/systems/apple/mac_mini/specs/mac-mini-core-i7-2.6-late-2012-server-specs.html
"This model simultaneously supports 1920x1200 on an HDMI display or a DVI display using the included HDMI-to-DVI adapter
and 2560x1600 on a Thunderbolt or Mini DisplayPort display or even a VGA display (with an optional Mini DisplayPort-to-VGA adapter, which is compatible with the Thunderbolt port)."
I got 2 of these 2012 Minis myself, using dual displays with them require using the HDMI port for one of the monitors, which as you see is limited at 1920x1200, even worse than DP. Over DP, since the machine does not support DP daisy chain, it is limited to a single 2560x1600.
I have never owned Apple Thunderbolt Displays, but it seems only this way you could chain up 2 2560x1600 TBD to fulfill that official Apple specs statement (Apple TBD uses proprietary / non-standard wiring to achieve things like this).
Regardless, even adding the total pixels of 2x 2k displays, it is still sizeably lower than what it takes to drive a single 4k display, at the same refresh rate. The "hacks" out there that manage to output 4k signal out of this Mini are essentially harnessing the total available graphical bandwidth of the machine, then concentrate them into one DP stream, at the expense of lower refresh rate.