Some of the auto choke models seem to do that when they have been just run for a short while. If you were to run it for a few extra minutes, does it seem better- or the same?

It's the same. I start it cold and run it until the bag is full and shut it down to empty the bag. Then every time I do this the black puff of smoke and very brief rough operation then runs normal. I'm just wondering if this will get worse or if the starting of the engine will get difficult if this goes on. Thanks

I would pop the air filter off and inspect to see if possibly there is a slight amount of fuel seeping up into the venturi or if the choke plate shuts instantly upon shutting off. there is a protocol of the auto choke operation on these. Seeing as though it seems to be consistent, it may best go into the dealer sooner rather than later.

mine does the same thing. ive never really worried about it

When the engine is cold, the auto choke closes and a lot of fuel is delivered. The cold engine needs this to start.

When the hot engine is shut off, the auto choke closes part way. When restarting, the engine is still hot and does not need the extra fuel.

See if there is a thermostat adjustment that will hold the choke open on a hot engine.

These engines are built for Kohler by a chinese factory. i believe they have some good features like a cast iron sleeve and ball bearings on the crank. The engines look massive, but only have 173cc.