My "guess" is it is running off of fuel that has expanded in the sediment bowl and ran down the fuel line into the carb due to heat off of the engine. (WELL ater you initially shut the valve off at the tank to "kill" the engine.)
Mine does the same thing . I TOO kill my engine by shutting off the valve and running it out of fuel. But the next morning I can pull the starter rod and it will take off running for several seconds.