Your app should show a 10-minute timer when you start the car, and the car will shut off after it hits the full 10 minutes. As stated above, you can only do this twice. Once you've started your car up for two 10-min segments, you will have to manually get in and start the car before this feature resets and allows you to remote start twice again in the future.
And yes, all Lexus remote starters will turn your car off completely as soon as you open a door. This way no one can break into your car and drive off, as well as the above reasons.