The delay relay should only kick the fans on after shutdown if the engine temp at shutoff is 226F or greater. The delay relay is triggered by a thermal switch on the intake manifold. If your fans are running after you shut the car off, and it's not 226F or hotter (I certainly hope it's not!) You have a problem. It could really only be one of two things.
1. The coolant temp switch (the one on the intake manifold near the fuel pressure regulator) is stuck closed. Check continuity between the terminal on the switch and a ground, if it's closed and the temp is below 226F the switch is stuck.
2. Your delay relay is messed up. A common problem, they're not sealed from moisture like the actual fan relays so they flake out from time to time.
What I did on my car was run a jumper between terminal F on each relay, that way both fans always turn on simultaneously, no matter if the A/C, ECM, or CTS switches them on. I put a switch in my jumper wire so I could revert to OEM fan operation by turning the switch off.
You can also run a wire from terminal F on each relay to ground and put a switch in line so you can work the fan(s) manually. I didn't do this, I just wanted the ECM to turn on both fans at the chip's 175F set point. The ECM only switches on the D/S fan at the chip set point, and on hot days the single fan didn't do that great of a job.
The little writeup on my webpage is
HERE.