That's why as soon as they're a week or so old and can jump a bit I but their food in a bowl that's about as tall as they are and only fill the bottom of it. That way most of it stays in the bowl. They still poop in it, but it still lasts longer.Mine scratch the feed everywhereI feed them and 5 minutes later there's no food left. But they're so cute so I let them get away with it.
Edit: I'm thinking about ordering a few more of those waterers to use for food. I have used them for food too, but since I only have two of them I usually end up using them both for water.