That sounds about right but honestly it's the plug that tells the tale. You'll prolly always have a bit of gunk comin' out the exhaust and while the choke is a better telltale - it's also an effective kill switch on a well tuned carb if the engine is just warmed up *shrug*
Synthetic oil can have a different coloration on the plug's electrode - but ashy white is lean no matter what, black & oily/heavy deposits is ofc too rich. With a non-synthetic it should be a coffee/tan - my synthetic seems to like a darkish gray.
Also - alla these lil 2 strokes 4 stroke a bit, particularly when new and/or not under load. They improve with time/mileage so if yer still under 300 miles I'd not worry the carb too much