My only source for this is a PBS documentary on Italian-Americans that I happened to see last week, so take this with as much salt as it deserves.

First, it is important to realize that there is a big difference between northern Italy and southern Italy. The difference was reflected even in how Italian-American immigrants were racially classified. When Italian-Americans came through Ellis Island, they could enter "Northern Italian" or "Southern Italian" for their race. If they were from northern Italy, they were considered "modern." If they were from southern Italy, then they were considered superstitious and backwards. Frankly, they were even considered racially inferior. As outlandish as that may sound now, this was in the nineteenth century and early twentieth century. As late as the 1920's, Calvin Coolidge actually closed the borders to Italy, saying that southern Italians were not capable of mixing with other races. There was huge discrimination against southern Italians.

But the discrimination didn't really extend to northern Italians. Northern Italy has Rome, Milan, Florence, and Venice. For whatever reasons, wealth and power have historically concentrated in northern Italy.

Meanwhile, the southern Italians have suffered. Of course, before the unification of Italy, there wasn't really a concept of Italy. Italy wasn't a unified nation, but rather a collection of kingdoms. In fact, the Bourbon dynasty controlled the kingdoms of southern Italy, so southern Italy was run by the Spanish, not even by "Italians" (again, the concept of Italy didn't really exist then). And the southern Italians were essentially serfs. They fought with Garibaldi, thinking that the unification of Italy, with its concomitant dissolution of monarchy, would benefit them. Of course, it didn't. They were just as oppressed as "freemen" as they were when they were serfs. The new government taxed them exorbitantly.

And--the documentary contended--because they had no control within their society's institutions, they built strong families, groups that they actually could have power within. Presumably, these notions of la famiglia influenced the formation of the Mafia, the Mafia often being referred to as "the family" and the dons positioning themselves as fictive kin, as "godfathers."

Most Italian-American immigrants were from southern Italy, because the conditions in Italy were so deplorable. They could not place any trust at all in higher authorities. If the government even knew that a person had a personal garden, that person could be taxed higher. So, the southern Italians became very secretive, too. Hence, perhaps, we get omerta, the code of silence.

Perhaps surprisingly, New Orleans was the first city where Italian-Americans concentrated, not NYC. After slavery ended in America, there was a huge demand for people to collect sugarcane. Southern Italians filled that demand. And, as there often is in poor communities, there was a lot of crime in the Italian enclaves. One police chief, Chief Hennessy, took a hard line approach against crime--especially Italian crime. But one night, Hennessy was walking home and a group of men gunned him down. Famously, his right-hand man rushed to him and asked him who shot him, and he said, "The dagos got me."

After their police chief was murdered, New Orleans police ran a dragnet, rounding up every Italian man they could find, whether they had any evidence of his involvement or not. To justify their action, they claimed that the men belonged to a criminal organization known as the "mafia." This was the first time that the word "mafia" entered the population consciousness. Because the police chief of a major city had been assassinated, the rest of the country was paying attention to the news reportage, which reported on "vendettas" being settled. (They preferred to use the Italian term, to highlight the otherness of the Italians.)

It might be worth noting that the Mafia had, at its height, only 5,000 members. Before prohibition, the underworld was essentially Irish and Jewish. Italian communities had its share of criminals, but the criminals mostly preyed upon their fellow Italians. In NYC, the Black Hand ran a protection racket and, in a span of only 2 years, bombed ~30 businesses that had refused to be extorted, killing many innocent people. The Italian-Americans were very hesitant to contact the police, because they had learned to distrust authority figures, making them easy prey.

tl;dr The Italian government post-unification made southern Italians family-oriented and secretive.