Per the rules (~page 9)
During the next Action of the indicated type that requires rolling the Action dice, you have to reroll the Success die one time if it shows a Success on the rst roll. Discard the token a er resolving its e ect.
So the reroll token is only removed after being resolved.
It is only resolved if you rolled on that action, got a success, and then rerolled it.
If you roll or not initially is determined by how many people are performing that action together, how far they are going, and if there is the -pawn token.
Yep, assume the worst case scenario. It is not easy surviving on an island after a shipwreck, dealing with harsh weather, predators, and possibly cannibals, a volcano, or many other inconveniences.