Ah, I suspected as much. 

Related, the next-checkers thing is smart (I don't think flymake can do that), however, I was rather missing an after-checkers like thing. It would make sense if css-js-phpcs only got run if jshint/csslint didn't complain, but then I'd have to modify the existing checkers. As it is now, css-js-phpcs takes over from those.