Holy shit, Jax vs Eve is unfair

So apparently, Jax can completely evade most if not all of Evelynn's damage - Her E is dodged by his counterstrike, and her Q and R are both reduced in damage by it. Why is her E evaded by it? It's definitely not an auto-attack, and while it applies on-hit effects, I'd imagine it's in the same category of ability as Fizz's Q.