But WHY?!
Who do we know who
definitely time travelled ?
Sawyer, Jin, Juliet, Locke, Miles, Faraday, Charlotte, Froghurt and a number of other survivors were "unstuck" while still on the island.
The rest of the Island's inhabitants were apparently unaffected.
Jack, Kate, Hurley, Sun, Sayid and Ben did not time travel as they had left the island before it "moved".
Jack, Kate, Hurley and Sayid
did time travel when their Ajira flight back to the Island crashed. However, the rest of the passengers, including Ben, Sun and Locke's corpse did not.
Jack, Kate, Sawyer, Sayid, Hurley, Jin and Juliette all time travelled for a final time back to what they would consider the present day (i.e. the same time as Ben and Sun) when the nuke went off.
I don't believe it's related to candidate status. Kate is not a candidate but did time travel and there are many names on the list who remained static.
My immediate guess is that either Jacob or The Man in Black simply chose who would time travel and who would not.