So we have an "undeniable" shutter firing, as identified by you by its sound, yet no apparent picture was taken.
Let's settle for now on the undisputed observation, that a sound was emitted. The internet is full of reports from SonyAlpha users about such sound phenomena after power down, and a wide range of explanations is being given. The most detailed and plausible explanation of which (in my view) was given by this guy.
Of course you are free to believe any other explanation, which
Maybe we should first confirm, that the shutter indeed fired, after you switched off your camera.
What makes you believe, the shutter fired? Did the camera take an additional picture? Or did you possibly interpret a "sound" from the camera as a shutter firing?
Please provide more detail.