It actually could mean that the 12 V rail is governing the bulk of the power supply. I think I would put at least a minimum load on the supply with the highest product of V & I. It's unclear whether all of the other supplies require a load of some sort.
Without a load, the supply thinks that the voltage is higher than it really is. The manufacturer's of the supplies don't want to put the minimum load as part of the supply because it messes up efficiency.
Generally, the schematics of multiple supplies that I have see, agreed a bit ancient such ss the DEC PDP-11 and the Amiga generally put the effort into regulating one of them.
The 5V supply has always been a target because it's specified at usually +-10% or so, but now the logic supplies are less tied to a specific voltage than they used to be.
It's hard to guess what's required, but before I gave up totally, I'd put 10% of a full load on each supply.
One key will be the voltages of all of the supplies. Are they ALL in regulation.
Just a note about remote sensing. Usually in a lab supply that sports remote sensing, there will be a sense lead for (+) AND a sense lead for (-). This compensates for the resistance in the leads, usually up to a diode drop or 0.6V. You don;t want the supply to go way out of regulation so the sense lead sees 0.6V more when unconnected. This is to avoid things like putting 40V on rail that's supposed to be 5V.
5V supplies were typically designed with crowbars which would short the supply if the voltage went over a certain value. This was called overvoltage protection or OVP.