It's hard for me to guess what you know or how much experience you have with this sort of work. I looked over both links, and they contain good info for a technician. Lets go over some stuff.
The ATX PS will power the A500 alone, right? When connected to both A500 and A530, the PS makes a distress noise and nothing powers on. When powering the A500 alone with the A530 attached to the computer but not powered, a jumper will supply 12v DC from the Amiga to the A530's fan.
If these things are true, then I beleive your A530 power connector is probably wired backward and shorting +5v to ground through the side bus. Hopefully, the crowbar protection in the PS has prevented damage to the A530. This is an easy mistake to make when looking at a connector. Does the 2nd web page show the front or the back of the power connector in the diagram? Grin.
Anyway, don't take anything else for granted. There is a logical way to check and, if needed, correct the A530's power cable connector. 1. Mate the A530 (with cover removed and the jumper installed that makes the fan run) onto the side of the A500. 2. Plug-in and power the A500 ONLY. 3. Set your voltmeter to a DC voltage range that will show both 5 and 12 volts (Not Ohms, Milli-amps, or AC-volts). The next steps are tricky, use caution and a very steady hand. Be carefull to never let a test probe touch 2 pins at once. You can use the meter to bridge between the A530's power socket and the disconnected power plug, one pin at a time. 4. Connect one meter lead to the A530's socket, pick any pin. 5. Connect the other lead to the exact mating pin on the power cable plug. Do this for each mating pair in turn. If you ever see the meter move, the signals on that pair is mismatched and causing problems. If one pair is mismatched, another pair must also be. If the meter "pegs" in the wrong direction (negative values), reverse the leads.
You can cross-check like this. Connect the black (negative) lead to the ground plane on the A530 circuit board. The ground plane is usually the large metal areas that have mounting screws going through them. Probe the socket with the red lead and record the values on a hand-drawn sketch. Do the same on the cable side and compare for like signals. Naturally, the pins that carry ground and shield will show no voltage (Gnd and Shield are connected together in the power supply). When everything matches in the power plug and socket, it should be safe to reconnect.
This is obvious, but, anytime the PS makes a distessfull sound, power off immediately. It's hard to put the smoke back into a computer once you've let it out. Grin.