It is a good example of bad statistics.
1. The study uses the 50 states as its baseline comparisons of "increase of foreign born" and "above-average employment rate" -- despite the fact that Rhode Island and California hardly belong in the same universe with regard to numbers of either, their percentages are averaged and correlated in this study. You can only study data points if they belong to the same set. Using percentages distorts the effect of the differences inherent in the data.
2. Percentages themselves are usually described as "ordinal numbers dressed up:" -- the second place finisher does not do "50% worse" than the first place finisher, despite that well known relation between one and two. Running averages and plotting them, as done in this study, is a disservice to learning things. Absolute numbers are available, and would make a better statistic. With percentages, you should present data as to the confidence level, as well as weighting by the base, after adjusting the base to comparable groups. The study of employment outcomes is not adjusted for population ratios of families with young children or retired people: and these two numbers have an affect on the percentage employed in each state.
For an example of a better study carefully done, check out this. Result? For the part of the worker population which has not graduated from High School, immigration causes problems. For everyone else, immigration makes us better off. What does that imply from a policy point of view? Well, the vast majority of US workers have graduated from High School, and therefore, as a society, immigration is a net benefit to us. We might benefit from more emphasis on High School Equivalency Exams for the part of our population hurt by immigration.