Rewatch the season 5 episode "He's our you" if you want to find out how Radzinsky knew about the crash of Oceanic 815; that the Losties knew about the Swan and had been inside; and the rest of the general future information which led him to continue pushing the button. Looks like Station7 may have been correct (at least about Radzinsky having a plan), even though he didn't find this piece of info. Radzinsky knew, and may have been part of the plot to bring the Losties to the Island. Could be why the Others allowed him to stay after the Purge, and why he continued to recruit people.
For those of you who don't want to or can't rewatch the episode: Sayid tells Radzinsky, Horace, and Oldham all about the future, including the fact he's a time traveler. They wouldn't have had to do much figuring to put together the rest of the Losties were time travelers, as well. Very interesting piece of info, IMO. I was gaping at the screen while rewatching this scene. Can't believe none of us remembered this little tidbit, me included!