The only possible explination was the others came in contact with the man who lied to Sawyer and got him to kill the innocent man thinking it was the real Sawyer. Or maybe Sawyer told someone and the others got to that someone. To my knowledge Sawyer hasn't told anyone on the island about that man he killed. However, he has told Kate he killed someone before he got to the island.

__________________
I Asked the reverand was the strip club cool ~
If my tips help send a pretty girl through school