I have no idea what Melasma is, but when I use urine topically I prefer it to be very fresh - it's still sterile. I suppose that others have their own preferences but I like it fresh. Doesn't urine start converting to something akin to ammonia when it is left sitting?
I don't like leaving the urine on my skin either, mainly for the smell issue. I find that leaving the urine on for a few moments then showering as normal works fine for any fungal problems.