Zinc is a terrible metal to make coins from. It's highly reactive and looks ugly after even just a brief time in circulation. It's only used because it's (a) cheap and (b) has very few practical uses; it's therefore not a critical "war metal" and so it often appears in wartime coins.
Zinc has some peculiar chemistry. When most metals oxidize, most of the compounds that form are black or dark-coloured. Silver, for example, tarnishes black, and iron rust is red-brown. When copper oxidises, most of the compounds are bluish or greenish in colour. Thus, corrosion on bronze coins is blue-green. But for zinc, most of the compounds are white; zinc oxide itself is familiar to Australian beach-goers as the white stuff in heavy-duty sunblock. White on zinc coins is therefore the equivalent of green on coppers, or rust on steel; it's a sign that some serious corrosion is taking place.
Zinc compounds are also known for being water-soluble. Thus, distilled/deionized water should work much better at getting rid of zinc corrosion by-products than it would work for other metals.
For me, the mystery isn't "why do some zinc coins turn white", but "why do most zinc coins turn black"? Apparently, the black is caused by a complex mixture of partially hydrolyzed oxides and organometallic compounds. It's not very stable, and thus not very good at preventing the "white death" from forming.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis