To minus1, if you have a turbo timer installe,d then yes it would be normal. But if you don't, both of you could be having the same problem but it can be from a variety of sources.
First off, pulling the EGI relay should be turning both of your cars off....
Second, make sure you guys have the newer style PTU, can cause a lot of problems if you have the old one, not sure if it would cause this though. this is the new one that you need:
then, here's the ignition circuit diagram for 300zx's. Check for shorts in the entire circuit.
Now, a problem i've seen is that someone has a short in the fuel injector harness, which then causes the ECU to malfunction and cause an issue like this. in this case it would be wise to find that short...
Then replace the ECU as well, as it can get damaged by the short in the injector harness.