Long before that. Spaniards in Mexico started carting Peruvian silver across the Pacific, in order to trade it for Chinese luxuries (silk, porcelain, lacquer furniture, etc) as early as 1565. The crews of those Pacific trade galleons, especially for the eastbound trips, were mostly not Spanish but Asian. And after a hard and dangerous journey across the ocean, it was common for sailors to jump ship and not go back to the sea, at least not right away. So you had communities of Filipinos and Fujian Chinese in New Spain, building ships in Acapulco, making faux porcelain in Puebla, and working as goldsmiths in Mexico City. By the 1620’s, Mexico city had its own Chinatown, and a Dominican monk complained that Chinese goldsmiths in Mexico City had driven Spanish goldsmiths out of business.
Spaniards were hiring Japanese samurai to put down Chinese rebellions in Manila in the early 1600s, and when Japan closed its borders around 1630, many samurai were stranded outside their homeland. Significant numbers of them ended up in New Spain, where they became the only group of Asians permitted by the Viceroy to carry weapons - they were hired to patrol the roads and guard silver shipments against hill dwelling bands of escaped slaves-turned bandits.
Source: Charles Mann, 1493, Chapter 8.
Mann doesn’t talk about the reverse flow of people, but almost certainly some Aztecs and Africans forced to crew silver galleons going west were jumping ship in Manila. Multiculturalism goes a lot further back than most people think.