Hawkmoon - "provides a nice breeze for her tummy." - the Mesh is porous enough. Plant shade material is designed to allow airflow.
He calls is a swamp cooler, but swamp coolers work by evaporation. Evaporating water absorbs head in order to change state from liquid to gas, improving cooling over simply passing over a cold substance.
The water bottles make this a thermal mass AC system because the water doesn't evaporate. Well, they likely collect moisture until they start approaching room temperature, THEN the water collected will evaporate and provide cooling for a touch longer.
As for the water bottles, I'm guessing about 4 hours.