When a reaction becomes cooler, it is because it is taking heat from the surroundings and making the surroundings cooler. For example, if the two liquids were at room temperature and in a glass, they would absorb heat from the glass for the reaction to occur. This makes the glass cooler, and makes it cool to the touch.
Another way to think about it is the evaporation of water. When we sweat, beads of water form on our skin. Now, vaporization is clearly an endothermic process and therefore absorbs heat. We sweat because as the water vaporizes, it absorbs heat from our skin and the air around us, cooling ourselves down.