It's not much an alternate history when you change a single flag. To support any of the events you have decided you'll need to go back as far as you can until you can craft a time-line that supports your new time-line of history. If the CSA winning is all that changed - which seems to be be a very common trope in itself - and nothing else was effected then it's presumed that all the rest of the world is unchanged by this dice-roll and will continue on as it had been.