According to "Azuma Kagami" (The Mirror of the East), during the speech Masako HOJO gave to persuade gokenin, she named Hideyasu and Taneyoshi as gyakushin (rebellious subjects) and it seems that the Kamakura Shogunate viewed them as the central figures in Kyoto.
『吾妻鏡』によると、北条政子が御家人を説得する演説をした際に秀康と胤義の名を逆臣として挙げており、鎌倉幕府からは京方の中心人物と見られていたようだ。