You turn the alarm off by starting the car, because the ignition has an rfid-like close-range reader which only requires passive circuitry in the key. That's how you differentiate between a break-in and the legitimate owner.
My car has push start (like many new ones) & has no keyhole inside (it has one in door to open the door). Although it has a seat/slot for the whole key to go in, in case of low battery. I assume that will stop the alarm. :-|
My car is also push start and I have to hold the fob in front of the start button for a short while before turning on the car if the fob battery is out.