I'm not ready to accept the time-shift theory for Desmond. I think it may be that he had clairvoyant powers before but his confinement to the hatch prevented his use of them. Now that he's out, the "healing force" may be allowing them to work so he simply knows things that have not yet occurred.

__________________
Things fall apart, the center cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;

--Lines 2-6, "The Second Coming" by Wm. Butler Yeats