When we learn about Jim Crow laws and the 1960s Civil Rights Movement in school, we always treat the U.S. as if it was separated into a racial binary of black and white. We read about how there were "colored bathrooms" and "white bathrooms and etc. for black people and white people respectively. As an Asian American, I have never been able to figure out where my people pooped. How did other people of color fit into this racial binary? Were different people of color treated differently?
You need to narrow your question to get a meaningful response. Jim Crow lasts from the mid 1860s to the mid 1960s and is played out differently in different parts of the country. And the terms Asian American and Latino are broad. Cuban Americans in Florida have s vastly different socio-political place in the US than Puerto Ricans than Mexicans. Same with Vietnamese, Chinese, Japanese, Indian. And all of those can be further broken down into smaller and smaller units that will each have had their own unique experience during the 100 years of Jim Crow.
Well, I can't speak much for Latinos, but the term "model minority" was actually invented in a New York Times article in 1966 to describe Japanese-Americans and how they were well assimilated, hard working and successful, unlike "problem minorities"
Given the time and context of the article, we can pretty safely assume "problem minorities" means "black people"
By the end of the year a similar article was published regarding the Chinese.
It has been argued (and I tend to agree with it) that this whole "model minority" concept was essentially created as backlash to the civil rights movement, as a way to sort of shame blacks into accepting the order of the times.
While Asian-Americans did have their own civil rights organizations they were nowhere near as large or prominent of those of other minority groups, and the "model minority" concept with reference to Asians has been pretty firmly cemented into the American psyche.
So, if you want a TL;DR, Asians, and the Japanese in particular, were basically used as a shield by American racists who were terrified of the increasing intensity of the Civil Rights movement.
The funny thing is, by nearly all of the numbers touted by the "model minority" people, one of the most successful immigrant groups in America are actually African immigrants.
Hi! Fortunately this has been asked before; there's at least one good thread I found in a search of askhistorians on this topic, and there are likely some good discussions on the topic in a few other related threads.