The familiar assimilation story is one we've already referenced in this thread: that the people who came in from Europe (particularly southern and eastern Europe) greeted the already settled (because "native" isn't correct) immigrants who established the first towns and colonies with a willingness to learn English and to work. Dependent on the congruence between these incoming people and those who were running the towns, usually on phenotypical identity but extended later to religious and cultural ties, they were in or out.
According to Barrett and Roediger, various waves of European immigrants embodied an "inbetween status" because they were categorized phenotypically with negative attributions (e.g. greed, filthy, poor, morally corrupt, etc.) and that these attributions were tied to skin color, while at the same time, they were given (albeit exploitatively) opportunities to settle and achieve limited mobility. Mind you, for much of the late 18th century and up to the mid-19th century, Italians, Poles, Slavs, and Jews were cracking into that opportunity structure while clearly brown, nonwhite persons were rebuffed with various levels of hostility.
Unlike the classic story of moving here from 1890 to 1940, any time after that was pockmarked by a deindustralization and restructuring of global industry. Back in the day, you could learn labor skills -- and granted some got treated better, paid better than others -- and make your way up the factory ladder while getting by. We quickly forget that manufacturing and industry gave us economic booms in wartime. When peace hit, the factories died out. Again, I emphatically say that this country is so economically tired because we don't produce anything and we thrive more from service sector industries that are done cheaper and better elsewhere. (Believe me when I say I'm no corporatist; they're part of the problem.)
In any event, Portes and Zhou theorized that this "classic" story of dropping English, working hard, and becoming American actually explained so little of how different ethnic groups assimilated. In their model of segmented assimilation theory, they suggest that new immigrants encounter one of three possible trajectories.
In the first case, they'll achieve classic assimilation and economic advancement.
In the second case, they'll achieve downward assimilation because, having no means by the time they reach these shores, they get stuck in central cities that remain underdeveloped. Denied opportunities and exposed to embittered subcultural elements, they act oppositionally toward American dreams and culture because of their experiences with personal discrimination.
In the third case, some ethnic enclaves do fine and mobilize upward, but do so only through having solid ethnic ties, remaining locked within their enclaves, and generating their own economic mobility structure. Proliferation of ethnic marketplaces gives them a niche that is appropriated by other people which brings money in and keeps these families afloat.
The problem with comparing Cubans, Nicaraguans, Puerto Ricans, West Indians, and black folk is that all of our historical and contextual backgrounds are different. Yes, Cubans came to this country because they were really ready to become American. At the same time, they came with quite a bit of capital of their own to do startups; the first people to get thrown out during their Revolution was the upper-class. Nicaraguans could settle in with them given that they were just as anti-Communist after surviving the Sandinista affair. Puerto Ricans were phenotypically classified as black and had much less capital. They had to make their own enclaves. Same for West Indians. And black folk -- well, we didn't have a choice in coming to the colonies. We were dragged here for slave labor.
Regarding the OP, of course all of this is based on fear. But fear is nothing new. Like it or not, the Americans who have run our institutions, our economy, our politics, and our judicial system -- as much as we want to hate the British and strike our way out here -- we pretty much replicated their foundations of law and order and we did it with just as much vehemence toward those who would "threaten our way of life." Stoked by the fear of losing independence, "native" whites enacted increasingly restrictive immigration laws and routinely justified their treatment of non-native-whites with racism, pseudoscientific superiority, and xenophobia.