I have a Korad KA3005D, which has an "Off/On" button for controlling whether the output is delivering power. This works fine in terms of regulating the voltage during these transitions.
But, I've noticed that when pressing the mains power button, the voltages can involve significant spikes. (Attached is a capture of the voltages when turning off the unit, where the oscilloscope probes are connected directly to the PSU output leads.)
Is this normal in PSUs? I'm still learning, but am presuming that, given this, it is prudent to not have the PSU connected to the DUT when turning mains on or off.