Assuming the accuracy of the immigration numbers, which as the article mentions: "Immigrant advocates in New Jersey said the numbers appeared to be an accurate reflection of the foreign-born population and the second generation."
How can anyone really know the true numbers? I don't believe the census to be accurate as illegals, naturally, would want to avoid such an encounter. How do I know? Illegals tell me.
The methodology of the study seems sound: they looked at hospital birth records. It's not a census or estimate. And while there are women who give birth without seeking any medical help, I doubt their numbers are large enough to skew the study.
The group who did the study supports less immigration, so I doubt they have any desire to under-report the numbers.