That's how the game works. All actions are performed one at a time. And all triggered effects that rely on certain conditions being met are always checking to see if those conditions are fulfilled or not.
So
Swept Away sees the Wraith that is not exhausted, and its effect does not occur. Once the Wraith takes his first wound,
Swept Away then sees that he is exhausted and so its conditions are met and the Wraith cannot take anymore wounds.