A fielder can also use that bag to make a play at first. Example: Runner on first. pop fly to right field...runner fails to tag up and is running back to first base...RF catches the ball and throws to first base who is touching safety bag. Runner is out.
Another example - Dropped 3rd strike. Catcher is way to the right side of the first base line. First baseman can set up on the orange bag to receive the throw.
Several folks have given you the ASA rule reference. If any organization would have a different interp on the double bag it would be Little League. I'm sure there is someone who frequents this Forum who currently works LLSB and has access to both a current LLSB rule book and LL's interpretation regarding the play in your sitch and the double bag.
USSSA has no exception for a throw pulling the fielder onto the orange portion of the base. On the initial force out attempt of a batter runner, the defense must use the white portion of the base, unless the throw is coming from foul territory.