Reese won 15 NCAA team championships as the head coach of the University of Texas at Austin men's swimming and diving team from 1978 until retiring in 2024, having previously served as the men's head coach at Auburn University from 1973–1978.

As the team's senior co-captain, Reese became the first Florida swimmer to win five SEC individual titles in a single season — the 200-yard breaststroke, the 200-yard and 400-yard individual medleys, the 400-yard freestyle relay and the 400-yard medley relay.

After six seasons, Auburn had produced four consecutive top-ten showings at the NCAA championships, and in his final season at Auburn, the Tigers placed second in the SEC and NCAA championships, the highest finish in program history to that time.

Starting with his second year at Texas, his teams have won the conference championship every season (44 in a row as of 2023).

Some of his notable swimmers include Ian Crocker, Rick Carey, Brendan Hansen, Neil Walker, Ricky Berens, Josh Davis, Dave Walters, Garrett Weber-Gale, Eric Shanteau, Scott Spann, Aaron Peirsol, Jack Conger, Clark Smith, Townley Haas, Will Licon, Joseph Schooling, Drew Kibler, Caspar Corbeau, and Carson Foster.