Oakland Athletics

Tinsley was drafted in the first round of the 1987 MLB draft out of Shelby County High School in Shelbyville, Kentucky. He began his professional career that year with the Medford A's of the Northwest League. In 1989 and 1990, Tinsley played with the Madison Muskies of the Midwest League. In 1991, he was promoted to the AA Huntsville Stars of the Southern League, where he hit .224 in 92 games.

Cleveland Indians

On July 26, 1991, Tinsley was traded by the Athletics (along with another minor leaguer) to the Cleveland Indians for Brook Jacoby. He played with the Canton–Akron Indians of the Eastern League through 1992. Tinsley was then promoted to the AAA Colorado Springs Sky Sox to finish the 1992 season.

Seattle Mariners

Tinsley was selected off waivers by the Seattle Mariners on September 21, 1992. He spent most of 1993 with the Calgary Cannons in the Pacific Coast League, where he hit .302 in 111 games. Tinsley made his Major League debut on April 6, 1993, against the Toronto Blue Jays, pinch hitting in the fifth inning and remaining in the game to play left field. He walked once and struck out once in two plate appearances.

Tinsley collected his first Major League hit on April 11, 1993, with a ninth inning pinch-hit single off Baltimore's Gregg Olson, eventually scoring the tying run to send the game into extra-innings. He hit his first home run on July 21, 1993, off Steve Farr of the New York Yankees. In 11 games with the Mariners, Tinsley had three hits in 19 at-bats for a .158 batting average.

Boston Red Sox / Philadelphia Phillies

Tinsley was traded to the Boston Red Sox on March 22, 1994, for a player to be named later. He hit .222 in 78 games for them in 1994, while tying a club record by going 13-for-13 in stolen base attempts in his first full year in the majors. Tinsley opened the 1995 campaign with a 14-game hitting streak, while also making good on his first two stolen base attempts of the year to run his streak to a team record 15 in a row, dating back to 1994. Tinsley later had a career-best 15-game hitting streak from June 10–25, finishing the campaign with a .284 average in 100 games for Boston.

On January 29, 1996, the Red Sox traded Tinsley (along with Glenn Murray and Ken Ryan) to the Philadelphia Phillies in exchange for Heathcliff Slocumb and two minor leaguers. He appeared in 31 games for the Phillies before being dealt back to Boston on June 9. Tinsley appeared in 92 of the Red Sox' final 102 games and hit .245.

Back to Seattle

Tinsley was dealt to Seattle prior to the 1997 season, which was an injury-riddled campaign for Tinsley, who started 19 of Seattle's first 24 games, but was eventually sidelined in May with an injured right elbow. He was then activated on August 1, returning to the lineup two days later, but was placed back on the D.L. on August 21. He hit only .197 that season in 49 games.

Later career

Tinsley never returned to the Majors, but he spent 1998–99 in AAA with the affiliates of the Anaheim Angels, Montreal Expos and Cincinnati Reds. In 2000, he played in the independent Western Baseball League with the Valley Vipers and then moved to the Mexican League where he finished off the season.