I had a similar concern to the OP when I had two different tickets. One ticket was an expiring MYW and the other was non-expiring. Both were linked to my MB as were my FPs. I wanted to make sure that I used the expiring MYW days before using days on the non-expiring pass. I was given the same advice that minnime noted above ... go to Guest Services to designate which ticket the computer would use. I thought that would take more time than I wanted to spend. So, instead, I just brought the actual expiring MYW ticket (just like pre-MB days) and used it for park access instead of scanning my MB. That way, I was absolutely certain that the expiring MYW ticket days were being used. When all my expiring days were used, then I used the MB to access the non-expiring ticket.
Since linked FP info really isn't on the MB (the MB just points to the data on the Disney computer) my FP's were unaffected and were still accessible using the MB at the attractions regardless of whether I used a MB or a physical ticket for entry.
Yes, you need to carry the physical ticket. But, it saved the trip to Guest Services (which can have long lines some mornings) and I was absolutely certain which ticket was used at each park entry.