Tachibana is actually related to the historical Tachibana samurai clan
There are two Tachibana clans (the kuge or noble clan
from the Nara and Heian period and the samurai clan from the Sengoku and Edo period) but since the manga deals with the Sengoku period, it's likely that Tachibana is from the Tachibana samurai clan, who sided with the Toyotomi until the end of the Sekigahara battle where the Tokugawa Shogunate stripped the clan of their titles and land until Tokugawa Ieyesu gave them back for proving their loyalty. It's either that Tachibana is a descendant of the clan or a reincarnation of Tachibana Ginchiyo or Tachibana Muneshige.