The link below concerns the situation with foreign priests employed in the diocese of Little Rock. Although the link goes to the reliable website CruxNow, it originates from the likewise reliable official Catholic News Service.
Link Thirteen Priests in Arkansas face uncertainty over their immigration status.
The article is an excellent summary of the immigration status of many overseas priests who help in our parishes. I value the spiritual work of these priests, and I do not devalue them as mere externs or curates. However, because the topic is seldom explained by parish or Rockville Centre, I found this article illuminating.
There are other angles, such as incardination and excardination. I suspect that, in practice, incardination (belonging to a diocese) hereabouts requires U. S. citizenship, so the "extern" remains subject to the bishop in his home diocese.
Comparison of Catholics per priest in sending dioceses vs. the Rockville Centre ratio (1 priest for 3,387 Catholics) can be researched at catholic-hierarchy.org The sending diocese may have a surplus of priests (as I found one in India, and one in Poland) or may need the priest more than RVC needs him.
The history page at drvc.org/history is about three years stale, but it states that the diocese had 392 priests in active ministry, 223 diocesan, 107 externs and 62 religious.