After being drafted, Tate went to the Spokane Indians out of the Northwestern League to start his career. He made his debut on June 26th, but would only make five more appearances after throughout the 2015 campaign. He finished pitching nine innings, giving up three hits, one earned run, and totaling eight strikeouts. Tate finished his 2015 season in the South Atlantic League on the Hickory Crawdads.
In 2016 Dillon Tate started in the SAL with Hickory again, tossing 65 innings for them. In that time he posted a 5.12 ERA, 55 strikeouts, 27 walks, and 37 earned runs. Tate was then traded to the Yankees’ organization where he would finish the year still in the SAL, but on the Charleston RiverDogs. Tate got in seven games for the ‘Dogs, throwing 17 1/3 innings, giving up six earned runs, 15 strikeouts, and finishing with a 3.12 ERA.
After a full year of grooming from the Yankees, Tate had his best year yet starting with the Tampa Yankees in High-A, then finishing the season continuing his success in Double-A Trenton. Between the two he posted a career-best 2.81 ERA after 83 1/3 innings pitched (another career-high). In those 83+ innings, he gave up 26 earned runs, 24 walks, seven home-runs, struck out 63, and finished with a career-low 1.14 WHIP.