So, I still don't get the details of how this can happen.
We have EMIYA from Fate Stay/Night who gets summoned in a timeline that is his past (Shirou). He could also be from another timeline (I forgot). Still, he is from the future, which made the plot twist kind of cool once you figure it out.
Now for Samurai/Remnant, you have Assassin who is from a timeline that is a few hundred years after the game takes place. Huh?
I guess magic transcends time and space... then we get into the whole predestination stuff that some individuals are destined to become strong heroes that can materialize as spirits.