Having done a quick search of references to water in scripture most deal with women fetching water.
The odd one does mention men such as :
Ex 2:19 They answered, "An Egyptian rescued us from the shepherds. He even drew water for us and watered the flock."
This is the occasion when Moses came across the women being harrassed at the well. It comes across as a surprise to them that he "even" drew water from the well for them.
Lev 15:13 'When a man is cleansed from his discharge, he is to count off seven days for his ceremonial cleansing; he must wash his clothes and bathe himself with fresh water, and he will be clean
Here the man has to wash his clothes. Whether you would call this "domestic" or "ritual" washing as it was part of the Law.
Ruth 2:9 "Watch the field where the men are harvesting, and follow along after the girls. I have told the men not to touch you. And whenever you are thirsty, go and get a drink from the water jars the men have filled
Here it mentions that "the jars the men have filled" as they were working in the fields and they would need water to drink.
But otherwise as far as I could see in scripture it was always the woman that did the water carrying.
This continues today usually in Eastern and African cultures.
Though I have known a couple of Western men who the idea of even filling a kettle for a cup of tea was NOT mens work.