BBM uses both the stats produced by the player and the position where he started (or if he appeared as a pinch hitter.)
However, the stats are not tied to any position. If Scotty Jones has a 2-4 night starting at second base, but has BBM starts available at shortstop, it’s possible that the 2-4 stat line could be used when Scotty starts at shortstop in BBM.
NOTE: For Ultimate leagues, the stats produced from MLB starts are sorted by whether the MLB starting pitcher for that game is left-handed or right-handed.