In the Deus Report for Serengeti, under the side story "[B] Can you not remember me?". It shows you Former B's final moments after saying "2 years ago." This means Former B dies two years before the Rosso arc. And in Rosso's side story "[B] 1 Year Ago, Wimp's Building", James B asks Mind about the Former B he killed. If that conversation took place a year before the Rosso arc, then Former B is already dead, and the B you fight in Rosso is the same one you recruit to your side. There's a ton of other references to this timeframe as well in B's side story entries.
I see why you are confused though. The Deus Report does change depending on the character you use. I viewed all of them on Hades, who rarely created any differences. After looking into it, I realized: the game is trying to compensate for the fact that B is fighting B by making up a new story about how James B is fighting a different Former B. That's not the real story. If it were real, the Rosso Epilogue wouldn't make sense, because James B would have never been under Wimp's control or poisoned by Wimp. Nor would any of the side stories make sense,
For more proof: B official joins the Players (and Bi-Gwang) in Old Clock Forest > Background Story > Freelancer, New Player Recruit. In that skit, James B says both that he took medicine in Rosso AND that he was once a villain. If James killed Former B in Rosso and then passed out, as the B-Rosso story indicates, neither of those things would be true.
The real story of Give Me More Painkillers is what everyone else sees, Misma asks to transfer B to Lapin - that is James B who the Players just defeated. That is the real story.