*Unregulated* 12V so the 15.6V is fine.
An LM338 regulator on that power supply can handle voltages of 15.6V just fine (up to approx 35VDC). If plug is pulled from J2 and fuse blows then you have a regulator problem. Test and adjust things with J2 removed - accidently putting 12V (or 15.6V) down your 5V line will cause lots of mean and nasty things to happen.
I like to hang a 1 amp load on 5V supplies during testing & adjusting. A 5 ohm resistor between 5V and ground will work fine. But make it a BIG cement resistor as it will be dissipating a constant 5 watts and will get hotter than hell.