The Rose, Sugar, and Orange have conference tie-ins. Fiesta, Cotton, and Peach will be the at-large bowls. The tie-ins are as follows:

Rose: P12 Champ vs B1G Champ
Sugar: SEC Champ vs B12 Champ
Orange: ACC Champ vs Highest ranked remaining B1G/SEC/Notre Dame
Fiesta: at-large vs at-large
Cotton: at-large vs at-large
Peach: at-large vs at-large

That being said, if a P5 champ is displaced from their bowl game due to it being part of the playoff that year they will in turn take up one of those at-large spots. The highest ranked G5 champ will also take up one of those at-large spots. That means there could be anywhere from 1-5 at-large spots remaining depending on the year and situation. The Rose, Sugar, and Orange will never get at-large teams - they'll just fill in the spot with the highest remaining team from the affiliated conference. For example, if Florida State makes the playoff this year as the ACC champ, the Orange Bowl will then fill the ACC slot with the #2 team from the ACC instead.