It kicks in either after something like 2.5 seconds, or not (if it decides it won't do it at the moment because it wants to keep the engine running for one of the many reasons).
It's actually really easy to control: release the brakes a little bit but not completely (like a little 'reverse dab') will restart the engine without letting the car move forward. Once you have restarted it like that it won't consider turning off again until the next stop. I use this to 'prime the engine' (if you can call it that) at the lights before it turns green again, no delay.
My wife says: don't buy an X1 because it has start/stop, please do buy a gas guzzling proper large SUV instead (preferably with a V8 no turbo or direct injection, 2 tons of weight, aerodynamics of a brick, and a gear box with 4 gears max) so she can have the only X1 on the road.
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I personally can't wait to be back in SF so I can pull next to a Prius driver at the light, have the engine stop and have them look at the X1 thinking it's a hybrid (since their engine will also be stopped they will hear mine stop) and then I can laugh at them as I leave them in my dust peeling off when the light goes green... muhahahahah!