You know already that I do IFS with my T even though she likes EMDR better. She often tells me "that's not YOU, that's another part" when I bring up a part. For example, recently when I said I had a "bad part" who I was ashamed of, she asked me who said the part is bad, or something like that. I said " I do, or all of me; my Self, thinks that part is bad". T replied, "No, its another part who thinks that way". She said that my Self accepts all of my parts, and does not think any of them are bad.
My T has always worked with 1 part at a time, not 2 at once. I'm not sure who brings them up, her or me. Probably I do most of the time. Often the parts are blended; that's the word she uses. I don't know there's another part involved, but my T does, as in my example above. I think it's all "ME" but my T says "it's just a PART of you".
I'm not sure if this helps you or not. I think you need to tell your T that you could not identify a part B and see what he says. Tell him he went too fast and presumed too much. It could be that there is a part that is so blended you don't see it! IFS Ts are very good at identifying parts!
Good luck in your session.

I'm sure it will go better after you explain how you felt. Maybe print this thread for him?