i understand it as an SMPS managed with a initial step-down transformer for isolation.
it has multiple outputs.
while loading 5V supply (being in control loop ) and managing 15V is correct,
perhaps it could be done this way.
try to manage to change the control loop from 5 V to 15V line, change the resistor divider to get 12V output. Generally they use TL431 as controlling element. Then on, on it works with 12V perfectly regulated. Other voltages would reduce to the proportion.
BTW, can you check what switch mode IC they used as per the unit by physical check and identify the feed back section?
Any schematic or block diagram, in the user manual that you may have?