I observe this every day. I heat water by first pouring it in a pan (made of aluminium, not that I think this detail is important). I put the pan on top of a flame, originating from natural gas. After a while, the water starts producing very tiny bubbles along the sides of the pan (I assume the old age of the pan favors nucleation). And then, one second after I turned the stove off, the water in the pan starts evaporating.
This is not a coincidence, I observed it hundreds of times. I don't have a satisfactory explanation, although I thought of some. The phenomenon looks as if as long as the fire was on, a sort of mechanical tension was applied, but I would not have any explanation for that either. So, if I think about differences of temperature, I could suggest that the hottest water is at the bottom of the pan until the heating stops. However, I don't see why it would suddenly diffuse once heating stops.
I also thought about the air surrounding the water, that could be warmer as long as the fire was on, but I dont even know if warmer air would slow down evaporation.
So basically, I have no clue and this goes really counter intuitive to me. I should add that if I decided to let the fire on way longer, then the water would evaporate a little while the fire still on, but the water would be way closer to boiling than my usual recipe. I have not used a thermometer, but I know by taste that my water that evaporate after fire is off, is around 80-85°C when it's done (I know teas and coffees well enough to descriminate such ranges of temperatures).