What follows is a generalisation from the Australian experience (my experience - I'm a child of first gen migrants i.e. a 2nd generation Australian). For the first generation and some of the second generation this is true. Migrants often don't know the language, and don't have pre-existing connections in the community, so they tend to cluster in areas where there are more people like them (often cheaper places to live). Working, they are more likely to work for other migrants, prolonging the "bubble" and deferring the need to integrate. This generation tends to live productive if somewhat fearful lives - "look at those locals with their degenerate customs!", "They don't like us!", "Be careful! Don't trust them! They'll take advantage!". These attitudes are of course almost exact mirrors of what the locals thing about the migrants. Attitudes primarily born of ignorance and lack of first-hand experience with the "other".
The second generation - children of first gen migrants - go to school, the local language is the one they're more proficient with. Perhaps its true that this generation feels the weight of anti-immigrant feeling more than any other. Mainly because inside, they don't feel that different. They grew up here, went to school here, understand the local culture. They straddle a cultural divide. They bear the weight of anti-immigrant feeling as well as the parental expectations to stay within their original cultural norms. This is rarely achievable. This generation often achieves well due to the over-emphasis on "Get an education! We never had the chance! You have opportunity! Don't squander it!" They feel the burden to do better than their folks very acutely. For those that can't achieve academically, or in business, or in sport - they are easy prey for ethnically aligned gangs. They can "retreat" into their origin culture and use anti-immigrant sentiment to justify bad behaviour.
By the third generation (e.g. my kids), a lot of the anti-immigrant feeling has moved on... to the new groups of migrants. My parents came from Southern Europe to Australia in the 60s. They were the "wogs" and "dagos" of the era. I remember being told in primary school to "go back where you came from!", which confused the hell out of me because I was born in Australia. Now, people from my ethnic origins are considered part of the wallpaper here. No one thinks of them as anything other than Australian (ok, maybe a handful of hardcore racists). In the 70s, the southern Europeans were replaced as the anti-immigrant bogeyman by the Vietnamese. Then the Lebanese. Then the Somalis. Then the Syrians. With each wave, the crime wave moves to a new group. Within a generation (or at most 2), any such spikes have dissipated.