The fans should not run when your engine is not running even if the key is turned to on, however they will always run when you have the A/C switched on and the engine is running. You have some sort of electrical fault or bad temp sensor if the fans run under these conditions:
1) Your key is turned to off
2) Your key is turned to on, but the engine is not running
3) Your engine is running and cold, and the A/C is switched off (switch off before you start, there is a time/pressure delay if you switch off the A/C once the car has been started)
So if any of these conditions apply, I would check any fuses/relays that relate to the fans, and if those are ok, have your sensors/wiring checked. Anybody else with input as to further causes of that problem please post. Hope this helps.