Some people will screech that it's the Kingsford's, but you're getting basically the same from other brands....
It's the the starters & binders in the briquettes most likely.....paraffin & some other things are used to get the stuff to lite & light evenly & quickly & thereafter, burn evenly.........
Lump charcoal will be a bit different & mostly better, but I've seen brands of that be smoky too.....
'natural' briquettes (Stubb's & Royal Oak are some) are bound with, I think, vegetable matter of some sort & are a bit better, but then I see some people also say that Stubb's is too smoky.....
Not a heck of a lot to add.......BBQ is a smoky business & unless you're getting bad tastes in the finished food or bothering the neighbors terribly, drive on.....you're doing all the right stuff keeping it dry, etc.
Always helps to burn as hot as possible, FOR THAT situation......meaning, keep a clean burning fire for whatever temp you shoot for / cook at........and, get a good, hot start in the chimney, too......
In the WSM, that might have been the deal there, not too much wood, just a little lag in temps / burn that let it smoulder enough to be noticed......but you said it wasn't major, so..............N/P.....