Basically as you come to a stop using the brake, once the car has physically stopped, the engine will cut out. This is providing that the massive list of conditions such as temperature, battery and loads of other stuff has been met.
As soon as you take your foot from the brake the engine will start again, literally before you get your foot across to the accelerator, so a heavy right foot shouldn't make a difference. If you're using the brake hold then again, once you touch the accelerator, the engine will fire. It can be a very smooth operation and is no doubt better on economy but mine's practically un-silenced so tends to scare children and little old ladies when it starts with the obligatory bark.