(It is possible, however, that in finding himself trapped in the Swan during the Lockdown incident, Ben deliberately calculated a means to destroy the Swan, rather than passively acting out events he saw beforehand.)
This would explain how Ben was able to let Michael go on the boat after the discharge. Desmond wasn't previously able to escape by boat. But Ben knowing the sequence of events would allow him to plan Michael's "release"
On the Pala Ferry, Ben said to Michael "...we got more than we bargained for when Walt joined us". Perhaps Walt told Ben the chronological series of events that would lead to the destruction of The Swan.
Premonitions are the side effects of the scientific experiments on the island. According to Sri Lanka Video, The Valenzetti Equation effects the core factors of human life. We know that the Numbers are affecting everyone's life (especially Hurley's) on the Island. So the experiments concerning about changing the fate by manipulating environmental factors could have some side effects on people living on the Island, thus letting them foresee things before they happen.
Time on the Island is not as we know it elsewhere. Perhaps the people experiencing premonitions have actually already done what they are dreaming about. It would not so much be a premonition, but just a memory of a past occurrence.
All of the survivors, and possibly also the Others have premonitory abilities, though some may not currently know it.
The Island may only permit those with premonitory abilities to land on it.
This would explain why it has been so hard for the outside world to find.
The fatalities on the Island may be because the people who were to die could not see the future - therefore the Island killed them because of this. Or they were simply unable to prevent their fate.
On the other hand, the Island may grant its visitors this ability when they arrive.