Fulmer started 21 games for the Savannah Sand Gnats in 2012.[4] He went 7–6 during the year with a 2.74 ERA and 101 strikeouts over 1081⁄3 innings. Prior to the 2013 season, Fulmer was ranked by Baseball America as the Mets seventh best prospect.[5] He pitched in only nine games that season between the Gulf Coast Mets and St. Lucie Mets due to injuries.[6] He finished the year with a 3.33 ERA. Fulmer started 2014 with St. Lucie and finished the year with the Double-A Binghamton Mets. He started 20 games, going 6–11 with a 4.38 ERA and 87 strikeouts.
On July 31, 2015, the Mets traded Fulmer and Luis Cessa to the Detroit Tigers for Yoenis Céspedes.[7] Fulmer was named the Eastern League Pitcher of the Week for the week ending August 9, 2015. He started two games for the SeaWolves during that time and had a 2–0 record with 11 strikeouts and a 0.00 ERA. He led the league in strikeouts (11) and tied for the lead in wins (2) and ERA (0.00).[8] On August 28, 2015, Fulmer was named the Eastern League Pitcher of the Year, and was named as the starting pitcher on the Eastern League All-Star team. Fulmer is 10–3 with a 2.06 ERA and 112 strikeouts in 22 starts for Erie and Binghamton.[9]