Isaac played a significant role on Penn State's defense in 2022.
The redshirt senior could have exercised another year of eligibility had he desired.
The hiring marks Ciarrocca's third different Big Ten offensive coordinator job in four years.
The linebacker totaled 72 tackles, 14 for a loss, and 13 sacks during the 2022 season.
Mulbah will enter the transfer portal will three years of eligibility remaining.
The Nittany Lions earned high grades across the board following their Rose Bowl victory over the Utes.