Boarding the ships felt awkward, to say the least.
Khan's announcement had turned him into an invading force, depriving him of all the privileges connected to his noble status, political role, and species. The soldiers managing the landing area didn't know how to behave in his presence, but the situation was too messy, and no one had the authority or power to stop Khan, so they simply let him go.
Returning to the Leviathan didn't improve the awkward atmosphere. The Scalqa were fine, but the human soldiers managing the bridge understood the magnitude of Khan's announcement and felt lost. They were servant of his noble faction, but that had probably turned them into humankind's enemies.