You're assuming that "The Others" have no contact with people outside the island. The ones on the island could be on the front line, with the real leaders pulling the strings far away in cities such as New York & London.

They appear to have very sophisticated communications systems so it shouldn't be difficult for them to communicate with their comrades. Have you forgotten that Juliet was approached by Ethan and another man connected to "The Others" at her work place?

It's natural that they know a lot about the people on the island.