Originally Posted by riccnick
That is the fuel system de-pressurizing. The extra fuel is pumped back from the throttle body to the tank through a small return line. Every fuel injected car does this, some are quieter that others. Some are a constant whirring sound, others have a rhythmic "knock". Also, if it is not that, it may just be the CD player cycling. When you turn the car on, the CD player preps itself to be ready, whether or not you are playing the CD. When you turn the car off, it cycles back to a default setting. Sometimes this is confused with the fuel return noise and vice-versa.
You have the 2012 Impreza too, do you notice it? Both scenarios do makes sense though.