Even though Ming China was the largest and most powerful polity in this region, its power was not absolute. The Ming had to constantly negotiate (and sometimes fight) with neighbors to exercise their power in various places and over different people. Meanwhile, at home, the dynasty wanted all interactions with foreigners to show Ming subjects that their Emperor was universally powerful.
The leaders in Joseon, Dai Viet, and Japan were also negotiating both internal and external audiences. They had to interact with foreign powers in ways that got them what they wanted, but at the same time they needed to appear powerful to their own people. Often, this meant describing a situation one way to a foreign government and a different way to their home audience. Even in cases where there was a significant power difference, polities were able to make active choices about if, when, and how they engaged with each other.