How do you define majority? Because unless there are marriage barriers, I feel like East Asian immigrants would eventually end up intermarrying with the local population which would decrease the number of people who could be considered strictly "east asian". But I would say that a good idea is to not have the PRC come into power as they restricted emmigration up until the 70s.
Also, you would want a country in Latin America to be a really attractive place to immograte to. In order to lessen the xenophobia that can come from people encountering foreigners, you may want to make Spanish a really lucrative language to learn that provides lots of opportunities. So, I would recommend making the Spanish speaking world in general rich. That way, people in China, Japan, and Korea would want to learn Spanish before setting out to immigrate.
May want to make Japan a less desirable place to live in by making it more crowded, perhaps world war 2 could be averted, or at least any mass destruction of old Japanese cities, so that way a lot of old buildings are preserved to take up space that would be taken up by skyscrapers in OTL.
Also, it would be a good idea for China to have a really good reputation in this timeline, so that way people dont mind Chinese immigrants too much. Be a bad idea to bring in Chinese as extra labor as that would breed animosity.
Honestly, I'd say at best, we'll end up in a situation like the US, where it's hard to say if German , Irish, or English ethnicity is the largest as the two groups merged a lot.