So I was reading the rules for the hound's tooth arc on the little pamphlet that came with the ship, and I got the impression that his 180 degree arch fired through the rear. Did I missinterpret the infographic or does he indeed fire out his ass just as the slave one.

You've misunderstood. It's 180^o forward. Look at the slightly shaded area on the ship's base token.

Just where do you see rear firing arc here? Just because firespray had its auxilary arc facing perfectly 180 degrees opposed to its main one, its doesn't mean that each ship with auxilary shoots "out of its ass".