That's a . . . simplistic narrative. The forms of oppression that Asians in the United States have faced are substantially different than those experienced by blacks, and have largely focused on not being allowed here at all, as opposed to de jure and later de facto slavery and the economic fallout thereof. Asian-American history has largely been a matter of being grandfathered around and further finding the niches and loopholes around blatantly racist laws designed to exclude us from the success of other Americans, such as laws barring Asians from gold mining and land ownership. Asians have also found success in ventures that white Americans were less successful in due to cultural differences; for example, the use of large scale collective labor in establishing farming in California, which had rich soil but was poorly suited for the "small independent farmstead" methods that were the norm for white farmers.
More fundamentally, Asian success in the United States is a much more nuanced matter than people think, because the "Asian" demographic in the United States actually consists of two radically different subgroups: Chinese and Japanese families whose ancestors moved to the United States before the Asiatic Exclusion Act and have been in this country for well over a century, and other Asian groups who have only been able to immigrate under the post-1965 laws and generally have no more than 2-3 generations in the United States.
The fact is that Asian immigrants aren't nearly as economically successful as is commonly believed, this is simply masked by lumping all Asians together, and in particular by counting multi-generational established families alongside recent immigrants.