i noticed the fan thing right after i test drove my car at the dealership before acquiring it. i asked the salesman about it, thinking the engine was still on, and he reassured me that it was simply the fan cooling the engine - he even popped the hood and showed me where the fan was, and i could see it spinning quite rapidly to cool the engine
after 10 months of use, i observed that the fan always comes on after turning the car off if the temperature of the engine reaches some threshold point. sometimes it turns on for 10 seconds, and other times for 2 or 3 minutes.
one time i had parked my hch for a short while and was walking back to it when a man walking his dog noticed the noise coming from my car, thinking it was the engine still on. comically, he looked around the car, inside of it, and in the wheel wells to figure out where the noise was coming from, and his dog went crazy sniffing the front. finally, i walked up to him and reassured him that everything was fine, and drove off, much to his confusion.
don't worry about it, it's a good thing.
