Spanish language in 1492 was not the same as is today. Languages evolve with time, so this old spanish evolved diferent in America and in Spain during centuries resulting in the diferences that exist today, also Spanish is diferent even inside Spain, every region has its own dialects and the same happens in America. At the time of colonization using vos, usted, was more common as old spanish was more formal than is today. It's not like usted doesn't exist in Spain, you just use it as a formal way to talk to someone nowadays.

The historical differences in the Spanish language between Latin America and the Peninsula can be explained by three primary factors: a process in linguistics known as "leveling", the regional origins of the Spanish conquistadors who arrived in the colonies, and the negotiations and changes that took place in the Spanish language in Latin America over time between indigenous peoples, creoles, and peninsulares.

I am not as well-versed in the specific reasons about why ustedes/vosotros developed more common usages in respective regions, but I can give you some basic background. Vosotros comes from an older form of second-person singular, known as "vos" which was often used in formal settings. At some point, vos morphed into second-person plural to form vosotros in Spain. Some regions of Latin America retained the old usage of vos as singular (Central America and much of the Southern Cone for example). I cannot speak on the development of "usted/ustedes" and why Latin Americans tended to use ustedes exclusively as a second-person plural.

I can, however, answer the general ways by which the Spanish language evolved in Latin America and Spain, specifically the use of ceceo/seseo (the famous "lisp", although it's not actually a lisp). Referring back to factors I outlined above, the first factors at play was the specific regions that the Spanish conquistadors came from. Many of them came from the south, from regions like Extremadura and Andalucia, regions of Spain that don't tend to use the ceceo and instead pronounce both Cs and Ss as "s". People from these regions also tended to to drop the s in many of their words, pronouncing them like "Js" in Spanish or "Hs" in English. You're probably beginning to see a pattern here- many South American countries share the same accent characteristics from Extremadura and Andalucia (the Canary Islands also contributed a lot of the influences as well).

The second factor at play is a process known in linguistics as "leveling". The expeditions that carried the explorers and conquistadors to the Americas contained people from all over Spain and even Europe in some cases. In order to be mutually intelligible to each other, they engaged in a "leveling" of their accents and speech patterns, whereby they changed the pace, tone, and even the pronunciation of their language in order to construct a type of language that was understandable to all. This process continued upon their arrival in the Americas, where the Spanish language was further negotiated and changed as a result of the interactions made with indigenous people, especially once indigenous people began learning Spanish and developing their own ways of speaking as well.

Finally, we have to account for the unique changes in language over time that developed both in Spain and in Latin America independently of each other. In many cases, Latin America retained some older forms of speech that the Peninsula abandoned. But the converse is also true- Spain retained older forms of speech that Latin America abandoned. Over time, different regions incorporated the vocabulary of indigenous languages into their Spanish. Since Spain was largely free of these influences, it did not adopt these changes.