Considering Mace Tyrell, Margaery Tyrell, and all of her cousins had perished in King's Landing, Highgarden no longer had any ties to House Lannister. Willas Tyrell was now the new Lord Paramount of the Reach, and he had decided not to involve his House in the upcoming conflict, focusing instead on the Ironborn that were plaguing their shores. Since all the Tyrell cousins had perished as well, the roses couldn't tie themselves to either side and finally decided to cut their losses short. They probably intended to wait and see who would win the conflict between Aegon and Tommen. Once the victor was clear, they would simply bend the knee.