tbf I am surprised that they're this strong. Joseon is a land based power, and them getting to fight the Japanese on equal ground is quite surprising since Japan is supposed to be the naval power of the region. Perhaps they're just not very accustomed to a navy sailing to the home islands and fighting them there.
If Joseon has an army just as effective as its navy, it will probably win out of attrition, or just by shocking Moritora's armies and forcing them out of various places.
they were fighting in Umashima, which is right off of Kyushu. The Joseon shouldn't be able to be this close to Japanese waters in general, the people off Kitakyushu should be able to see them fighting if they paid attention.
tbf I hope we see him coming to his power during the war, and him continuing to fight for the Japanese afterwards in SEA would be very fun. For example, Koxinga being the general at the helm of conquering Palawan island would be very interesting.