Hard to say exactly what is going on without actually seeing what you're doing.

The choke heater is seeing power with the key off regardless of how you think it's wired. Depending on the wiring, it could be backfeeding from somewhere else.

You really need at least a test light (a multimeter would be better) to check wiring. With the key off, the test light should not light up when touched to the choke heater feed. If it does, you have power coming from some place. The multimeter is better because it will show a low level power feed that might not light a test light.

I would hazard a guess that the relay circuit you have is using a relay to power the choke so that the trigger can be hooked up to any key on power source without over loading the circuit.