After leaving the University of Kansas at the age of 20, Allison was signed by the Senators as an amateur free agent before the start of the 1955 season. After signing, he was assigned to the Hagerstown Packets of the B-level Piedmont League where he hit only .256 in 122 games. The following year, he was promoted to the Charlotte Hornets in the single-A South Atlantic League. Although he improved his power numbers, hitting 12 home runs and 6 triples, his batting average dipped to .233. Allison then spent 1957 and 1958 playing for the Chattanooga Lookouts of the AA Southern League and he raised batting average and slugging percentage to .307 and .446 respectively in 1958 (both highs in his minor league career). On September 16, 1958, Allison made his major league debut, batted lead-off, and got a single in four at-bats in a 5–1 loss to the Cleveland Indians.