The earliest baseball mention of a “southpaw” - as 
  found by Tom Shieber, senior curator at the National 
  Baseball Hall of Fame—appeared in the New York Atlas 
  in 1858, but in reference to a left-handed first 
  baseman, not a pitcher.

The first documented use of a phrase or term in print, does not mean that the writer used it according to the original intended context, especially since it does not specifically get used in a passage that explicitly states the intended use and origin.

The atlas doesn't explicitly state: "We decided to call him a southpaw, because we're inventing this new term, and not because of convention, and it means 1, 2 and 3, because x, y and z."