I agree, the puff of smoke is more than likely the valve stem seals. By not changing the seals, can cause carbon build up in the top end of the engine. Maybe causing shorter engine life. I read on another forum. subject being Honda eu2000i. It was claimed by a poster that his eu2000i had over 3500 hours on it and still running well. He had installed a hour meter when brand new.
If you are using two eu2000i hooked together to run your a/c. You might want to look at a soft start for you a/c. I have on my a/c and the single Honda eu2000i will start the a/c no problem even on eco
throttle. No brown, out just a smooth start on the ac compressor