They are in turn resolution order. The human is always player 1 and the AI's are players 2-x. The 'order' is decided by the setup screen - you'll notice the human player is in the first slot (player 1) while the AIs fill in the remaining slots. Normally the civilization of each AI is set to random and that's why the civilizations seem to be in a random order. If you manually set the civilization of each AI before the game is started you'll see that they appear in that order - for example set the AI slot just below the player to France you'll see Napolean at the top of the diplomacy tab.