How did the lord of Tsushima count as a Daimyo?

Reading The Making of Modern Japan, I read that the Daimyo of Tsushima, through whom all trade with Korea went, had a domain of 5,000 koku, most of which were from the Korea trade. Since daimyos were strictly defined as being those samurai with estates rating over 10,000 koku, how was the ruler of Tsushima a Daimyo?