Who paid for Columbus' journeys? What did they demand?
The Roman Catholic monarchs of Spain (the Spanish royal family) that paid for Columbus' journeys. In fact, they paid for four of them. All of which entailed a boating voyage over the Atlantic Ocean.
Under the auspices of the Catholic Monarchs of Spain, he completed four voyages across the Atlantic Ocean. Those voyages, and his efforts to establish permanent settlements on the island of Hispaniola, initiated the Spanish colonization of the New World.
In return for this valiant patronage, the Spanish crown expected that Columbus reach Asia via the East Indies by sailing towards the west. Navigation at that time, of course, was in its infancy. There was no way to know what land masses existed upon the earth until someone sailed it fully, and it was Columbus who discovered many new things in doing so. In fact, as the story goes, due to his mistake, and thinking America was actually the East Indies, Christopher Columbus mistakenly "named" the Native Americans "Indians," a term that remained "politically correct" until the late twentieth century.
Columbus' proposal to reach the East Indies by sailing westward, eventually received the support of the Spanish Crown, which saw in it a chance to enter the spice trade with Asia through a new westward route.
It is interesting that you ask what the "demand" was. It isn't like Columbus would be killed if he didn't succeed. He was just expected to try his utmost best. He did try his best, but he didn't meet the "demand" of the Spanish crown. Why? Because North America was in the way of Asia! As a result, he is credited with discovering the "New World."