If an engine is running near the pressure rating of the radiator cap when it's shut off, the heat soak after shutdown can overcome the cap spring and cause the reserve tank to fill and/or overflow. Running the fan after shutdown cools the radiator enough to prevent overflowing. A 15 PSI pressure cap will let the coolant get to 257 degrees before it boils. Most electric fans turn on at 220 degrees, and turn off again at 200. If the pressure cap is leaky, the coolant can boil before the fan ever starts to run.
Jerry