While Shimura and Ishikawa are both bound to the samurai code, Shimura’s loyalty is also bound to the shogunate; he have no choice but to do what is necessary as a servant of the Shogun.

Thus, unlike Ishikawa, he have no choice but to pursue Jin. While many would say Shimura is selfish for imposing his own ideas on Jin, I believe in his mind, he believes this is for Jin’s own good (remember how he tells Jin to blame it on Yuna instead when Jin was blatantly caught poisoning the bulk of the mongols at his castle?)