I'm wondering if you are in a hot, dry climate - here's why...
This happens to me a lot in Phoenix - a hot, dry climate. Seems like when the pile is fresh, the fungal nets grow. However, if the pile sits too long, the outside layers start to dry out, resulting in the "smoke" you refer too. I believe this is either dried fungal bodies or perhaps spores... Whatever it is, it can have a detrimental impact on some people's respiratory system. I suggest always wearing a dust mask or respirator if you're working with a pile that's dried out and "smoking".
If I know a pile is getting dry, I
water it very thoroughly a day or two before I want to spread it. This cuts down on the amount of "smoke" flying around. Note, it sometimes takes quite a long time for the water to penetrate through the pile.