When the batt is disconnected and it keeps running, the alternator keeps the car running.
The ignition, when cut off is supposed to interrupt electricity and the motor should stop.
Pulling the relay also interrupts electricity.

Possibly there is a difference in the wiring harnesses and that is causing the car not to cut off.
I would also check the ign switch. It's possible the switch is not interrupting the electricity.
Put a test light on the contacts and see if the switch is working.

You might also look on the i-net for a swap like yours and see what people are saying.
If everything is working except cutting the car off, some people would put in a manual
off-switch like race cars have.