Sounds like the terminal positions may be different in more ways than you're thinking. or maybe its just a diffrent type of relay and not correct at all.
Start wire to the relay should only be hot when key is in Start.
The start terminal that wire attaches to should connect to ground. Through a wire to a safety switch or the case
I don't know what the 'G" terminal on some of the replacement ignition key switches is for. Don't use it. Maybe it is for ground, maybe its not. Test it on all key positions to be sure it doesn't connect to anything if you're curious.
Take some photos and post them up. It will be easier to see what you have.
