At the start of the turn, time moves forward by the clocks of the cards set that turn, including Compass Clock (Hunch Gray) and The egocentric password“ ”, and effects are resolved starting with the cards played by the priority player (the player on whose side the medal is after time has moved forward).
For example, if the player who played Compass Clock (Hunch Gray) is the priority player, "Return to the time at the beginning of the turn" is resolved first, then The egocentric password“ ”'s "Set the clock to midnight", so the Chronos ends up at midnight.