Physics/chemistry behind the observation This is purely observation based. Any time I have cooking something on the stove, if I change intensity in any direction - reducing or increasing the heat, it seems like water vapor threads shoot out from the pot.

I can understand if I increase the heat, more energy, but don't have any explanation for reducing the heat. It seems like state change any direction causes some water vapor to release.

Don't think it matters, but it's gas based stove.

What causes the vapor or threads of mist to shootout when there is a change ?
It's hard to say without seeing it, but I suggest that this phenomenon happening when you turn up or down the gas may be caused by your arm reaching out in the vicinity of the pot to turn the knob.  

The air above the pot should be saturated with water vapor at a higher temperature.  Motion nearby will create eddy currents that carry that moist air to where it can meet cooler air.  You see the moisture when it condenses to fog.