Tinsley was born in Texas and played collegiately at Baylor. He spent one season with the NFL's Los Angeles Rams before joining the Blue Bombers, where he often played both ways at tackle.
He is noted for a story regarding the 38th Grey Cup, known as the "Mud Bowl" because of poor weather/field conditions. "As the legend goes, Tinsley, a rookie Bomber lineman, was face down in the muck and water, gasping for breath when an alert official pulled him from his murky grave".
Tinsley died on September 14, 2011, aged 87, from undisclosed causes, in Winnipeg, Manitoba.