I was given the quest to "discreetly" kill the hidden vampire in Markarth. So I took him into the abandoned house where I killed him. While still inside the house two guards show up almost immediately and charge me with a crime. Excuse me? No one but Lydia saw it. Did Lydia rat me out?

Well how did you get the Vampire into the house?

Chickens. They see all.

They're also pretty big tattletales. They'll tell the guards anything.

I told him to follow me.

its still considered a crime if you kill someone while standing.

I killed a target for the Dark Brotherhood. NO one was around. not even a chicken so I walked up and killed him. got a bounty and then last witness killed, bounty removed message. I bet in your case you didn't crouch and just attacked him openly. you got a bounty and since the guards were just outside, they came in to arrest you.