It would seem that the others did not "remember" Rimmer being alive.
The "rules" of time-travel vary greatly between different sci-fi universes, but Red Dwarf has featured various different methods of time-travel with different results. However, within this episode, it is evident that those who make changes to history retain their prior memories.
When Lister successfully persuaded his younger self to patent the 'Tension Sheet', he, the Cat and Kryten all disappeared from their timeline (because the change affected them) but Rimmer remained and remembered everything about them and what they had done. This is why he proceeded to return to their "new" futures and undo the changes they had made.
When Rimmer undoes the changes in the timeline, returning things exactly as they had been before, the other crew return having no knowledge of what just happened, but Rimmer and Holly remembered and understood what had happened. It is Holly that notices Rimmer is still alive, and presumably, when Rimmer quickly dies again, Holly also resurrects him as a hologram.
The comedy punchline is that the others are not aware that Rimmer has just died, so it could be assumed that they never know. If holograms are generated from a 'backup', Rimmer's new hologram may only have been able to pick up his memories from prior to entering the Timeslide, and he may not have remembered his second death. Therefore it is possible that only Holly remembered all the events.