Power supply voltage climbs after disconnection
This is only a guess, but I will propose the following hypotheses:

Hypothesis 1)

The supply is rated to deliver 10 "Shenzen Commercial Amps" which seems to equate to about 3.5 Real Amps as you noticed when the voltage sagged under load. Then something inside blew up. This seems to be confirmed by the fact the supply is now acting weird.

Hypothesis 2)

The supply's transient response is slow. When the current drawn from your load abruptly switches from several amps to zero, the pass transistor takes a while to turn off. If capacitance on the power rail is insufficient, this will result in a voltage spike on the output. It should not produce lasting damage however, so this wouldn't be my favorite hypothesis.

Hypothesis 3)


The PWM stops, and the FETs all turn off.
The FETs are off, thus they act as rectifier diodes.
The motor keeps turning due to inertia and acts as a generator.
The generated voltage is rectified by the FETs and fed back into the supply
The cheap chinese supply dislikes this and something inside blows up 


Now with a 12V supply the motor would reach a cerrtain rpm, but it wouldn't go fast enough to generate a lot more than 12V... unless we consider its internal resistance, which will matter due to the high current. When it acts as a generator, you will get its unloaded output voltage, which can be more than the original supply voltage, because the current is now very low, so the internal resistance matters less...

You should manage the motor stop, maybe leave the bottom FETs turned ON until the motor has stopped completely, I'm not sure.