The following June, with the Reading Fightin Phils, Quinn suffered a torn hip flexor that kept him on the disabled list for the remainder of the season.

Quinn was instead assigned to the Lehigh Valley IronPigs, where he suffered a torn ligament in his middle finger, before being called up to the Phillies at the end of July.

He played through the end of the season with a broken pinky toe, but missed Opening Day the following year due to a preseason oblique strain.

[4] In 2011, during Quinn's senior year of high school, Baseball America named him the fastest man in their Top 200 pre-draft report; he had a 6.35-second 60-yard dash speed, and took an average of 4.20 seconds to run from home plate to first base.

Because he did not sign with the Phillies until the day before the MLB deadline for college-committed players, Quinn could not start playing professional baseball until the 2012 season.

Sports journalists in Williamsport took notice of Quinn's "put the ball on the ground and run" batting style and declared him the "Human Highlight Reel".

[8] He was assigned to the Single–A Lakewood BlueClaws to start the season, and on April 9, Quinn hit an inside-the-park home run in a game against the Hagerstown Suns.

He spent most of the season as the Threshers' leadoff hitter, batting .257 with seven home runs, 36 RBI, 32 stolen bases, and a .343 on-base percentage in 88 games.

[17] Quinn recovered from the injury by October 15, the start of the Dominican Professional Baseball League season, and joined the Tigres del Licey.

Once again, his season was hindered by injury: Quinn strained his abdominal oblique at the plate on June 4, and returned to the field prematurely ten days later.

He made his major league debut on September 11, 2016, playing in center field and batting second in the order against the Washington Nationals, and went 0–3 and drew a walk.

[23] The following day, in a home game against the Pittsburgh Pirates, Quinn hit two doubles, stole a base, drew a walk, and drove in two runs in a 6–2 victory.

[26] When asked about his plan for 2017, Quinn told reporters, "My goal is to stay healthy, man, just to be honest with you", and expressed his frustration at never playing a full season of baseball.

[9] After appearing in spring training with the Phillies, where he was evaluated for a possible major league position in the outfield or at shortstop, Quinn returned to Lehigh Valley in 2018.

[30] That May, Quinn tore a ligament in his right middle finger while diving into a base, and spent several weeks on the disabled list to recover from surgery.

[32] Three days later, manager Gabe Kapler chose to give Quinn the start over right fielder Nick Williams for a game against the Boston Red Sox.

[33] In the first game of a doubleheader against the New York Mets on August 16, Quinn and fellow position player Scott Kingery were required to pitch the final innings of a 24–4 loss when the team ran out of available relief pitchers.

[45] On September 21, Quinn and manager Joe Girardi were both ejected from a game against the Nationals after arguing with home plate umpire Junior Valentine on a called third strike.

[46] In the 2020 season, which was shortened due to the COVID-19 pandemic, Quinn played in 41 out of 60 games, collecting two home runs, seven RBI, and 12 stolen bases, as well as a .213 average.

[26] Going into 2021, Quinn became part of a battle to start in center field, competing for the position with Kingery, Odubel Herrera, new signing Travis Jankowski, and prospect Mickey Moniak.

[48] On May 26, while attempting to round third base in a game against the Tampa Bay Rays, Quinn collapsed on the turf, falling again when he crossed home plate.

[49] He appeared in 28 games before his season-ending injury, recording a .173 average, two RBI, and four stolen bases in 52 at bats, while on defense he had a 1.000 fielding percentage with two assists.

Quinn, shorter than many of his teammates at 5 ft 9 in (1.75 m) and known for his speed while running the bases, drew early comparisons to retired Phillies shortstop Jimmy Rollins.

[7] During the 2020 season, Quinn led the MLB in sprint speed, capable of running 30.4 feet per second (9.3 m/s), an improvement from the previous year's 30.1 ft/s (9.2 m/s) average.

[2] Former MLB outfielder Kenny Lofton helped Quinn develop a batting style that would take advantage of his smaller frame and rapid speed, allowing him to compete with larger, slower power hitters.

He emphasizes bunting, line drives, and other batting techniques that slow down the speed of play, thus allowing Quinn to safely reach base, whereupon he can attempt to steal.

In 2018, Quinn, his wife and children, and his extended family, were impacted when Hurricane Michael hit the Florida Panhandle, including Port St. Joe.