Without getting too much into stuff.... There were plenty of Chinese and Japanese going to Argentina and Brazil in OTL. Have them all move north for safety (especially because of the conflicts in Republic of Tupi-Parana), and that might be the result.
Also, remember Alberto Fujimori? He's a member of the second largest ethnic Japanese population (90,000) in Latin America after Brazil (1.5 million). Since I excpet there to the hostilities between the Japanese states and Peru around the turn of the century, all those immigrants could go northeast in search of safety.
But in OTL, most of that immigration seems to have started in the 1900's--if similar patterns hold in this world, the trend is very recent. If there are tensions between Peru and the Japanese states at around that same time, then South America would not be an attractive destination. (Indeed, you might get "Japanese Exclusion Acts, or similar.) Why not go to the existing North American Asian diaspora states?
But let's say there was more immigration, or earlier, or both. Regardless, the previous inhabitants of this northeastern state are probably not going to be thrilled when they are swamped by these refugees. It's a small country, not like the OTL US or TTL Peru, so opportunities are going to be limited. Unless conditions in Peru, Tupi-Parana, and all the other countries in South America are
ludicrously bad, I think a lot of the Asian immigrants will stick it out. (Discrimination in the US got pretty bad, but did everyone move to Cuba in response? No. Offhand, I can't think of any parallels to the sorts of movements being suggested here...)
Now, maybe an Asian-plurality state, with a lot of those being recent immigrants fleeing anti-Asian pogroms in an unspecified nearby country... that I could maybe see. There will be political tensions out the wazoo between the newcomers, the Europeans, any Africans, and the surviving natives. I don't think it would be a fun place, or a safe place... but it could be an interesting place, and maybe a plausible one.