Besides the Zeus' power of deciding to end the turn prematurely, he also fills the vacated space when the ship moves.
Does he choose the "adventure disc" to be placed, or merely selects one at random?
Per the rules:
Zeus now chooses a new adventure disk from the reserve and places it on the empty space where Odysseus' ship started the round.
I think the word "choose" is a clear indicator that it doesn't have to be a random disk. Especially as it's specified to be a "face-up reserve"!