Ants drink the water, put it in their social stomach, and then vomit out the excess if need be a distance from their nest. It's basically their version of a bucket bail line. It's a real thing, you can look it up.
There are also some other things about their nests such as air flow which could be causing it. Most ants use their thermal mass to heat air, this causes the air to rise. Genetically they are programmed to dig a combination of shorter tunnels vertically and longer tunnels horizontally. The result is that hot air rises out of the nest fast, and vacuum is then filled by cooler air from the tunnels that open farther away horizontally. The result is a passive temperature regulation, specifically a form of moderation, and that air movement can dry the pile out as dry air becomes humidified.
