Thanks for that, it is gives a better understanding of what you have, your construction looks quite good.
I am not sure how much reliance to put on all those declarations of conformity on that power supply but the big one that is missing is the UL mark. It is not surprising as it is perhaps the hardest one to obtain with respect to a power supply. UL is largely driven over concerned with the device starting fires, hence the name Underwriters Laboratory, it arose from insurers wanting to minimise their risk. I do know that UL has a much stricter limit on the earth leakage current than some of the others like CE. I am not saying go for a UL rated power supply and it will solve the problem, they are a lot more expensive and the UL rating mark might be false on Far East designs.
What it doesn't change is my guess that the problem is probably due to earth leakage and the best bet is to have things connected up before applying the power. I know this means powering down then up before making changes to things, but that is what you should do anyway. Even plugging a monitor into a computer that is running can damage things. Their are things you can plug into a computer when it is running, like USB but they have been specifically designed to be "hot swapable", these designs connect the power rails before connecting signals.
I have a similar problem with the Raspberry Pi, you can't plug many things into the GPIO pins without resetting the computer. In the case of the Pi that is a bad thing, because its main storage is an SD card, and unexpected interrupts runs the danger of destroying the card. And being Linux the boot up process is not swift.