I have the files but they were from WOTM5 which just had final spoiler go up but isn't closed yet. Can I upload the files yet or would that not be ok?
I'd hold off until the game closes, or a mod says its OK.
I just rechecked my save and this doesn't seem to me to be what happened.
The way I see it:
Cultural Victory
1) I have almost enough culture to win but I'm not there yet. I do any moves and hit end turn in turn X.
2) Turn X+1 comes up with the flash screen that says I won a cultural victory. I can't do anything but it is definitely turn X+1 not the previous turn - I can see the changed year. Movie starts and finishes etc.
3) Turn X+1 comes up again and gives the "more turn" option. I press that and see that I am still in Turn X+1 which is the year I won. I never moved any troops - I have all my moves left etc since it is the beginning of the new turn.
I think that what you describe is exactly what I describe, but we have a different sense of what is meant by the turn of the win, and the turn after the win, so it seems different.
Let's say you build a warrior. You first get to move it on, say turn 20. Did you build it on turn 20? That is what I used to think. But if you look at how the logs record items, it will say you built it on turn 19. That is because the warrior was completed by the hammers that you got at the end of turn 19 (after your moves, so you could not move him in turn 19).
Research is similar ... logs say you discovered X on turn 19, and began Y on turn 20. But to the player, it seems like you discover and begin next on the same turn.
So with that in mind, you really achieved the cultural conditions on turn X, even though the game will say your victory is turn X+1. You didn't see that you met the conditions in turn X because the final steps of turn X (the AI turns and the addition of hammers, culture, etc.) do not occur until you are done with your part of turn X. I think of these as interturn events.
So when the instructions say submit the save of turn after victory, I assume they mean save of turn X+1, since they consider victory to have been in turn X (even though the game will credit the victory to turn X+1). But in one sense, since the game says victory is turn X+1, then turn after victory ought to be X+2, which is what I think your question arises from.
The idea of X+1 being the turn after victory is more clear in a conquest or domination victory. There, it is clear during your turn X that you won in turn X (you get the pop or land right away, or you killed the last civ). So X+1 is the turn after victory (again, even though the game credits the victory to X+1).
Hope that helps.
dV