When you turn off the key....you have turned off the ignition and there is no more spark to ignite the fuel/air mix.

As the engine continues to rotate - it is still pulling air through the carb and it is picking up fuel and still creating a fuel/air mixture....and that fuel/air mixture gets pumped through the engine and into the hot exhaust.

The fuel/air mixture in the exhaust gets hot - and when it gets warm enough and reaches the flash point - it is ignited in the exhaust system and makes a "POOF".