Let me give you a 3rd option which is what we do. Pitcher's know the day ahead, minimum, that they will be throwing a pen and who the catcher will be. Those two or four, we have double pen, know that they have no set up job that day and there job is to come out stretch warm up and throw their pen. Bullpens are coordinated so that they are done by the time the rest of the team is done stretching and throwing.