If you leave a bowl of water in the open it will eventually disappear due to evaporation and lose heat whilst it's doing it.
The evaporation process only takes place at the surface (or water/air interface) and takes energy from the water to turn it in to water vapour. The vapour is then free to join the rest of the water vapour in the air and carry off that vapour and the energy (heat) it contains thus reducing the energy left in the water (dropping the temperature).
Things that have a major effect on the speed of evaporation is temperatures, surface area , relative wind speed and humidity. So by squirting water through nozzles/holes to make fine droplets you are hitting two of these parameters.. You are maximising the surface area of the water and using some of the energy from the pump to accelerate the droplets and thus increase the relative wind speed.
As for night verses day. Humidity (or more importantly relative humidity) is a governing factor. The hotter air is, the more water it can hold before you reach dew point and the stuff starts to condensate back out. As the air temperature drops over night you will reach a point where the air can take no more water and thus the cooling process of evaporation stops and you may even see a mist on the surface of the water where the water vapour is converting back to liquid and condensing out.
So night time cooling will only work if there is not a mist of condensate. I hope this very simplified explanation of what's going on helps........