It could be that doing something similar when he was a stray/feral got him some type of attention that he liked. Maybe he thinks he's setting aside a "gift" for you when he does that.
Maybe it changes the taste of the water slightly, and he likes it better that way. Does he do it pretty soon after the water's changed? Does he do it when the water's been sitting for awhile?
It's also possible that he's setting it aside for later, and then never retrieves it because when "later" comes he realizes he doesn't need it, but hasn't been able to unlearn the behavior. That type of thing is very common with former strays and ferals; they learned that there was no way to know when their next meal would be, so they ate all they could whenever food was available, and maybe learned to hide some or set some aside for later. Even years after adoption, they can't seem to unlearn that tendency.
It could also be that he's a cat and cats are bizarre like that. lol I'd say see if you can identify a pattern with it. See if there's a particular time that he does it, like when the water's fresh or when it's not-so-fresh. Maybe try praising him and showing him approval immediately when you see him do it, to see if how often he does it changes. If you can find some type of pattern, then you might be able to figure out why he's doing it.