Brother if you're pissing straight ammonia you've got other problems. Your body specifically coverts ammonia to urea because it's toxic to you and it's usually bacteria that converts it back.
Huh, the ones I've seen always say to flush thoroughly, and I've been told it's to prevent a potential buildup of residue from clogging the toilet or bursting a pipe. Maybe that's outdated info, or because of a different formula? Wouldn't be the first time some old wisdom doesn't apply to modern products anymore.
It does happen, you just don't get that much of a reaction because it's diluted. You definitely don't want to stick around the fumes that it gives off though.