Question is it up to the firstbaseman to choose to use the orange(runners)bag if the ball carries on a play and in turn then it is the runners responsibility to use the white bag?
Answer Essentially yes. If the play is coming from foul territory, F3 should set up on the orange side of the base in plenty of time to allow the runner to understand that they need to use the white portion.
If F3 is set up on the white portion of the base, they can't switch to the orange side in reaction to a bad throw and expect that the runner will be put out.