Looking at this from a simple perspective... inside cat vs. outside cat is a very different thing weather they know the cat or not. As other have said, he was just acting on instinct. Don't judge him too harshly.

If you plan on taking him outside, try and make sure your other kitty is INSIDE.

King was good with cats inside, but outside cats were still fair game to him. (And this is a dog who loved everything under the sun and refused to kill... almost everything. I think he would have only chased the outside cats, but i never gave him the chance for me to find out.)