As you can see in the screenshot below (full size here) my own settlement (Moridunon) has white "fumes", whereas my ally's city (Iska) has green ones. But my enemy's settlement (Eblana, far left) doesn't have any fumes – nor do all of my own cities.
So at first I thought it had something to do with population growth, but that seems unlikely. Something to do with diplomacy seems unlikely as well, because then I would expect my enemy's city to be red.
Best Answer
The white fumes happen when a city is building or upgrading a building. The green sickly fumes mean that the city has been hit by a plague. Looking at your picture it looks like the fumes are comming from the army so this would mean that it is actually the army that has been hit by the plague and not the city itself.