Rules question

I am sure I have seen the answer, but need to be reminded.
If I have JJ. Putz as a SET UP and Closer: Not before 8th
He will NOT tire if he comes in during the 8th and then becomes the Closer in the 9th.
What is the rule here.
Is this correct?? Do the settings re-set once he becomes the closer??? and then the fatigue factor kicks in for his closer rating???
If I have JJ. Putz as a SET UP and Closer: Not before 8th
He will NOT tire if he comes in during the 8th and then becomes the Closer in the 9th.
What is the rule here.
Is this correct?? Do the settings re-set once he becomes the closer??? and then the fatigue factor kicks in for his closer rating???