So this is likely to take a while to figure out, with others asking you questions and having you make measurements or do things while we puzzle out what is going on with your car.
Question 1: Did this just start happening, or did you just buy the car and some prior owner may have janked up the wiring before you got it?
Measurement 1: After operating the car to the point that the passenger side fan comes on, leave the car running and go listen to the fan. Now turn off the ignition and listen again. Did the fan speed slow down and get quieter? (I'm suspecting not.)
Action 1: See if you can download a good copy of volume 4 of the 944 workshop manual (electrical) and locate the schematics for your car. The '83 will be the first set of schematics. Neither link I have has a good copy. This link has a copy with some pages in reverse video for some reason:
944 Workshop Manuals
This website has a copy from an '84 which is very very close to an '83, but the center of the fold out schematics is missing. Still, better to have around than not.
https://www.pelicanparts.com/944/electrical/944_electrical_diagrams.htm
The radio and a/c ventilation systems do not share any circuitry, I have no idea what is going on with your car (bad ground somewhere is the usual first guess.) Lets concentrate on getting your engine cooling fans working first.