There doesn't have to be an MCU involved. Ordinary logic gates or even linear circuits can result in the same thing... capacitors hold power which can illuminate the lights and the signals controlling the lights drop into "indefinite" states. Depending on the specific nature of these states, the lights can be switched on for a moment.
Normally, such behaviour is completely ignored as it does not represent a valid condition of such circuitry (You know ... it's just been turned off!)
There is the situation where such light flickering (of lights or whatever) IS an issue. In those cases, special design considerations are made to ensure the circuit behaves as required in all circumstances.
In a number of situations, power sequencing - both powering up and powering down - is vitally important. Some lab supplies have such functionality.