Both, you throw them and the bottle breaks letting the potion touch whatever it is that you are killing. And its so true, that is why I ran out, I had to defeat a ton of them. I was able to escape because well, they were in little pieces.
Yeah, they tried to break down my door. Luckily enough I kept them from getting in. I had to cut an arm or two off of a couple zombies, but I'm fine.