Have you set the follow me home function in Idrive? I seem to recall it's under settings>lights.
The car is switched off in two stages. Press the start stop button once and it turns off the engine. Press it again and it turns off the car's electrics. It's akin to having the 2/3 stages on an old ignition barrel with the first stage allowing you to run the car's electrics without the ignition being primed or the engine running.
Drives: F30 320d Luxury. On order: Glacier Silver 430d M Sport