You have to look both at the situation and the dynamics. There are two reasons for the increase in pressure: air trapped in the jar gets heated and expands, and warm water evaporates, increasing the pressure by adding the partial pressure of the vapour to the atmosphere inside the jar.

Now. Put down the jar, screw on the lid. You have a particular mass of air at ambient temperature, plus a mass of fairly still, hot water with a fixed surface area. Pretty soon the evaporation heats the air mildly, increasing its pressure, until the water surface, which is nearly flat, but slightly concave (iow a slight meniscus) cools to the temperature of the heated air. A concave meniscus is an unfavourable shape for water to evaporate from. There is of course some convection, but slight enough that the temperature of the water surface is lower than its internal mass, and that surface temperature is the temperature that the air is in contact with.

Open the jar, and there is a slight exhalation; nothing dramatic.

But shake the jar and your water - air interface is very large, with large numbers of convex droplets from which energetic molecules escape, giving up most of their excess energy very quickly. There is not much water, warm or cool, that does not make contact with the air very quickly. Both the available heat and the available water rapidly attain equilibrium with the air temperature and partial pressures, so it is hardly surprising that there is a pop when you remove the lid!