The ONLY way this happens, is that your ignition system is still getting power from somewhere after the switch is pushed. Now assuming that you DO have the kill on the positive lead... with the switch pushed, obviously that power is not coming from the battery.........so that only leaves SOMETHING attached to the alternator circuit somewhere. Since none of us can see the car, you are going to have to track it down. Start chasing wires and circuits is the only answer. You say the ONLY thing on the lug of the alternator is a big wire running to battery and NOTHING else. If that is true, the "field" wiring is supplying power to the ignition. Appears you must have a Mopar alternator, so to "fix" it, you will have to break the field circuit as well when you kill it. That is why some were telling you to use a relay. The field circuit runs through the relay and battery power switches the relay on. Kill the battery, relay opens, breaks field circuit

Monte