This is part of the Pre-Third Impact Instrumentality. Right before the kitchen fight, Shinji and Asuka witness a scene from Misato's college days, where she is having sex with Kaji. Shinji clearly has never seen this before asking "This is Misato? She does... this?" in which she replies "Yes, this is also me... The melting into one another's hearts... The me that Shinji doesn't know." If this entire sequence was all "in Shinji's head", there is no way he'd know these things. Instead, because he is already in Instrumentality, he has access to Misato's memories. This also applies to the preceding Hell Train scene.
I don't really understand what 'Pre-Third Impact Instrumentality' means. I don't picture how Shinji could interact with Misato and Asuka prior to Third Impact, specifically the lowering of AT fields and the mingling of consciousness. The entry for Instrumentality seems to agree that Instrumentality occurs as a result of Third Impact, so it is not existing prior to Third Impact:
Human Instrumentality would arise as a result of the Third Impact, resulting in all Lilin souls being gathered into Lilith's Egg and united as a single existance. This would create a state of being for humanity where no individual existed; even identifying this being as a conglomerate would be incorrect, since there would be no such concept as an individual. To achieve this extreme homogenization, the flaws in every living being would be complemented by the strengths in others, thus filling the gaps and erasing the insecurities in people's hearts.
So I am not sure I understand how there could gave been an authentic interaction between them unless the scenes preceding the Komm Susser Tod sequence are nonlinear and occurred during Third Impact somehow. That doesn't quite make sense though, since the culmination of the kitchen scene and the following dialogue with Rei seem to be what pushes Shinji to wish for Third Impact to occur.
I just don't really see how Shinji could access the real Misato and Asuka at that time unless the scenes are nonlinear to what we see occurring in real time. Shinji is in a unique position of being in Unit 01 at the time, so his AT field would be lowered sooner based on what is said, but I still don't expect he could interact with others until the souls are gathered together during Third Impact. I do agree the dialogue sounds like it is between the real characters, but I'm trying to get how that works. My best guess is that it has something to do with the fact that both Misato and Asuka are dead at that time - I certainly don't think everyone was experiencing Instrumentality prior to Rei/Lilith lowering the AT fields of the living.