All the conditions need to be right for the alarm to remote start.

There is a button you need to press on the remote, whilst the engine is running, then you get out, arm the car and after a few seconds the engine will shut down. The alarm knows that because the last time it was running, the alarm was armed, therefore nobody was in the car, it will leave it primed ready to start. Providing the alarm didn't go off, the system is happy that nobody could have put it in gear, so you press the assigned button to start it.

What remote do you have? How many buttons does it have?