I will speak from the perspective of one who emigrated to the US.
Every new group is initially seen as "the other". After some point, however, employers that hire "the other" may find that they can pay them less because there is less demand to hire them, and thus benefit financially, they hire more. As other employers follow suit, over time the salaries go up until they match that of other groups.
Their children benefit. The first generation of manual laborers and farmworkers begets the second generation of policemen, nurses, and soldiers begets the third generation of doctors and lawyers and professors.
In the US this has happened to Irish, Italians, Germans, Russians, Jews, East Asians, Indians, and Latinos. Why hasn't this happened to blacks (or has happened in substantially less numbers), despite the latter having the benefit of US citizenship and command of the English language from birth? Why hasn't this happened to the Somalians mentioned elsewhere? The Muslims of Dearborn?
Or look at Britain, where you have three groups from the Indian subcontinent:
* Indian Hindus
* Indian Sikhs
* Indian and Pakistani Muslims
Sikhs and Hindus have been very successful; they are more likely than the average to be part of the British middle class <http://www.theguardian.com/money/2010/dec/14/middle-britain-...>. Muslims are, by contrast, worse than average in every single social measure despite being, racially speaking, indistinguishable from the other two groups to any outsider (since none knows, or cares, about the myriad of caste differences); they are all "Asians" in Britain. But the outcomes are completely different.
I will ask you the same question you posed. Are these differences in outcome the groups' fault? Or the host society's fault?