Being a displaced Irishman I heard "cat" too - a very southern Irish pronunciation approximates [cash] with a very light touch on the sh sound - just like Dutch kaas, in fact.
After half a dozen tries, however, I did hear "kaas".
Keep listening, fishystikky! It will happen!
I do not remember - and maybe never really knew, but I would surmise that it is because the sentence is making an assertion about the the relative positions of the milk and the cheese, and this is somehow different from saying that the milk is on the table (in which case staat would be used) or in the fridge (in which case zit would be used).
I don't think there's such a thing as "aanachter". In another exercise, I think the verb was "aanrennen", though, which means "to approach by running", or "to chase", e.g. "De hond rent achter de kat aan". I'm guessing "aanrennen" can't take a direct object (or if it can, then it would have a different meaning), so "achter" is used to link the action of the verb to "de kat", just like "after" could be used to link "run" or "chase" to an object, e.g. "The dog runs after the cat".
Edit: See comment below. It seems "aanrennen" isn't a verb; rather, there is phrase, which is basically "achter [something] aan".