McAllister graduated from St. Viator in 1926, and was elected the "head coach of athletics" immediately thereafter. He coached the St. Viator football, basketball and baseball teams from 1926 to 1930, and compiled win-loss records of 46–14 in baseball and 51–19 in basketball in four seasons.
McAllister later served as the head coach of the Florida Gators men's basketball team of the University of Florida in Gainesville, Florida, from 1937 to 1942 and again from 1946 to 1951, leading the Gators to an overall record of 119–96 in ten seasons. McAllister was also the head coach of the Florida Gators baseball team from 1940 to 1942 and from 1946 to 1947, and compiled an overall record of 40–56–4 in five seasons. During his stints as the head coach of the Gators' basketball and baseball teams, he also served as the line coach and assistant for the Florida Gators football team under head coaches Josh Cody, Tom Lieb and Raymond Wolf from 1938 to 1942, and again from 1946 to 1950, while doubling as the head coach of the Gators' freshman football team known as the "Omelette Squad."
National champion Postseason invitational champion Conference regular season champion Conference regular season and conference tournament champion Division regular season champion Division regular season and conference tournament champion Conference tournament champion