I've found there is a very specific sequence about putting the car in park, taking off your belt and opening the door which results in the car shutting off (not stop starting, but shutting off) the engine and you get the ignition on. This is the same behavior you'll get with pushing the start button (when car is off) without your foot on the brake. If you hit the right sequence the car shuts off as you found, if you do not hit the right sequence it keeps running as you expected but did not experience.
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