Basically, everyone in the lobbies in isotropic are marked as new, just won, or just lost. Players who just lost are given first priority when the site determines turn order, and players who just won are given last priority. (In the Dominion rulebook it states that when playing multiple games, the player seated to the left of the previous game's winner goes first--in other words, you win a game, you go last in the next one.)
I don't recall if new players (who just entered) are matched up randomly with everyone, or the other rules still apply. That is, I think if someone new plays someone who just won, the new player will always be first player. But I'm not sure.
Also, if people are in the same group (new/just won/lost), the ordering is random.