No the power supply provides only 12V, there is a subsequent transformer actually on the ATX plug. This is what powers the interface board, the fan and the Pi. It could well be that which is blown, at least partially
Are you sure? There are yellow wires for all 12V related components (including the controller board) and a red wire from a different connector on the PSU connected to the controller board (through the plug you speak of IIRC). I assume the red wire is 5V as it's the standard coloring for this voltage (at least on PC equipments) and I don't see the reason why 2 separate 12V lines would be connected to the controller board with 2 different colors.
Edit: maybe there are different a2mini generations with different power supply solutions?