Seems pretty straightforward to me. They had been the exact same Kathryn Janeway until just a few hours before, so the differences between them were insignificant, only a matter of the different circumstances they were in. So when Janeway said "there was a part of me that could see her point of view," that was literally true, because the "her" was, in fact, another part of herself.
And Tuvok did not say both
Janeways were at once the doubter and the doubted. He said "One could say that you were both the doubter and the doubted." In other words, that both of the arguing Janeways were still the same single person.