Tinnion began his career in 1965 with Workington A.F.C. which then played in the Third Division. However, the team dropped to the Fourth Division in 1967. In 1968, he transferred to fellow fourth division club Wrexham A.F.C. During the 1971–1972 season, he played three games on loan to Chester F.C., but otherwise was a regular first team player with Wrexham during his eight seasons in Wales. In 1976, he left Wrexham for the United States where he signed for the New York Cosmos, playing alongside Pele. He played one season in New York before being selected by Team Hawaii in the expansion draft. Hawaii lasted only one season before folding and the Colorado Caribous picked him up in the dispersal draft. He played twenty-four games with Colorado, scoring four goals in 1978 before being traded to the Detroit Express. The Express left the NASL following the 1980 season and moved to the second divisionAmerican Soccer League. In 1982, the Express won the league title as Tinnion led the league in scoring and was named the league MVP. That season, Tinnion coached the team as well as played midfielder. However, he was not listed as head coach as the league prohibited player-coaches. The league changed the rules in 1983 and Tinnion was named the official head coach for 1983 and 1984. Tinnion also spent 1980–1981 Major Indoor Soccer League with the Wichita Wings.
Coach
After retiring from playing, Tinnion remained in Detroit where he continued to coach. In 1990, he was hired by the Detroit Rockers which played in the National Professional Soccer League. He was named the 1990–1991 Coach of the Year. The next season, he led the team to the league title. In December 1994, he resigned from the Rockers to become the head coach at Eastern Michigan University until the university dropped men's soccer in 1999. In December 2001, Tinnion returned as the head coach of the Rockers, but the team folded at the end of the season. His son, Paul Tinnion, was head coach of the Eastern Michigan University women's soccer team and is now Director of Coaching of the Michigan Jaguars soccer club based in Novi, Michigan.
Current
Tinnion now lives in the suburbs of Detroit with his wife Mary and his two sons, Joey and Kyle. He previously coached for the Michigan Revolution, Workington and the Grosse Pointe Mustangs.