In 1984, Allison moved to the United States to attend the University of South Carolina. Between 1984 and 1987, he was a four-year starter on the Gamecocks' soccer team. He led the Gamecocks in scoring each of his four seasons and holds the team's career scoring record with 63 goals and 32 assists for 158 points. He was a 1987 First Team All American. Allison graduated summa cum laude with a bachelor's degree in physical education and a minor in biology in 1988. He played professionally for one season in Ireland.
In 1989, Allison became an assistant coach with the North Carolina Tar Heels as he worked on his master's degree in physical education, recreation and sports science. In 1991, he returned as an assistant coach with the South Carolina Gamecocks. In 1995, Furman University hired Allison as head coach of the men's soccer team.
In 1991, Allison was named the National Outstanding Physical Education Teacher of the Year.