I use it for my 13" Pro Retina....and I like it but it is a little loose but fine. My guess is it would be a little loose on a Air...so if you don't mind the extra room it will be fine. If you want a snug fit, this is probably too big.
It is not QUITE as tight as I would like on the 13" but it is very, very close and it works just fine in a backpack, etc. I really don't think a 15" would fit in there without really, really stretching it.
Well, I strongly believe that this sleeve would fit your 13.3 inch July 2013 MacBook Air. The sleeve would be too big tho,, but it doesn't mean you cannot use this sleeve for you laptop, it would be just too big, you know. If I were you, I would prefer the sleeve that is specifically designed for MacBook Air or MacBook Pro Retina Display and not this one. Hope this helps!