It’s entirely possible (by which I mean extremely likely) that pitchers like Papelbon, Kimbrel and Hader do worse in the eighth innings than ninth is because each of them, as the best relievers on their team, are almost exclusively brought in early to face tougher hitters. I bet vintage Kimbrel never came in early to face the #8 hitter on the opposing team. Maybe to face the guy pinch hitting for the pitcher. But probably more often because someone batting 3-4-5 was due up.
However, in the ninth innings, they face enough 7-8-9 hitters that the damage done by middle of the order bats gets absorbed into their stats with minimal impact. But with fewer 8th innings, the damage done by the more potent hitters becomes a larger part of the sample.
Or you could simply believe that they are just magically better one inning later…