Correct…. Said it was a “step up” from a swamp cooler
There are also systems that drop a suction hose over the side down into the depths to siphon up colder water and run it through a heat exchanger then circulate the cooled air… same basic idea less the ice.
Its just fun to look into the various options available … there are multiple different takes on the same basic desire to cool off.
Back in ancient Egypt they used a drum with a top side lip to provide a portable fountain.
The drum had two holes with one being a pipe from just above the drum bottom then up the center and above the top lip and the second being at the top of the drum lid below the lip. Fill the drum with water, plug the hole in the top lid below the lip. Place in the sun and allow to warm up. The expanding water flows up the pipe and burbles out and collects in the area of the top lip. Resetting is accomplished by pulling the plug below the lip allowing the water to drain back into the drum. The cooling portable sound of water flowing in the desert several hundreds of years BCE!

People have always been smart!
Wet curtains in open windows with a breeze blowing through was probably something that goes back into pre-history…