In 2015, Thompson pitched for the Single-A Quad Cities River Bandits and the High-A Lancaster JetHawks, registering a 3.00 ERA with 60 strikeouts in 43 total appearances.

The following season, Thompson split the year between Lancaster and the Double-A Corpus Christi Hooks, recording a 3.35 ERA with 65 strikeouts in another 43 appearances.

In 2017, Thompson played for Corpus Christi and the Triple-A Fresno Grizzlies, logging a 4.05 ERA with 61 strikeouts in 66+2⁄3 innings pitched across 37 games.

[citation needed] The Tampa Bay Rays selected Thompson in the minor league phase of the Rule 5 draft on December 13, 2018.

[4] Thompson spent the 2019 season with the High-A Charlotte Stone Crabs and the Double-A Montgomery Biscuits, recording a 2.70 ERA in 16 games between the two teams.