Yes, when the very first save file is submitted for a game, the GMR website will make sure that the civilizations selected on the website are the ones set in the save file. So if the host creates the HotSeat game differently than how the game is defined on the website (either the player order is different, the civilizations are different, or the AI/Human selection is different) the website will directly modify the save file, setting these values accordingly. So for example in our
Speed game it seems that something was a little different than how the game was set on the website, because while everyone is technically playing as the correct civ, their colors are off. This is a current side effect of the website changing a player's civilization after the game has already been created. We actually have an idea of how to fix this for future games but haven't had a chance to implement it yet
Oh, and if a player has selected "Other" as their civilization on the website, then instead of enforcing their civ in the save file GMR will update the website to reflect what civ was selected for them in the hotseat game.
It's all a little complicated, but I hope my explanation made some sense. Please let me know if I can clarify things further!