John was late for work. His colleague said James (the manager) was looking for him. When John walked in James' office, he said "Are you looking for me, James".
In the above context, I think John should say "Were you looking for me, James"? Am I correct?
I agree with you. If John had walked into the building and had interrupted James during the search, he could have said "Are you looking for me, James?"
Note that when a question is being quoted, the question mark should go inside the quotation marks. I have marked the relevant corrections in red above.
Let's say that James started his search for John at 9.05am. At 9.10am he finished searching the first floor of the building (without finding John) and then went down to the ground floor where the main entrance to the building is. At 9.11am, John's friend sent him a text message saying "Where are you? James is looking for you!" John entered the main entrance at 9.12am and spotted James walking along a corridor looking in offices. He ran up to him and said "Are you looking for me, James?"
James had not finished his search but John stopped him while he was searching, thereby "interrupting" him.
Does that help?
I'm not a teacher of English, but I have spoken it for (almost) all of my life....