When you say it "stays on", you mean after you turn the AC off, yes?
The std Ran fan is attached to the engine, so it's obviously, always on.
As for the AC one, remember it's an overheat fan, so your car could be running at 91+C and triggering the fan that way.
But don't be scared by the word "overheat", 91C is fine (your temp needle in the instrument cluster doesn't hit "Hot" until closer to 110C), it's just used to help out the clutch fan in hot weather etc.