No such exclusivity exists. The federal government has the authority to set forth a uniform rule of naturalization. Nowhere does it say the States are powerless to police immigration. They can make laws and enforce them as long as they don't contravene federal laws.
This has been explicitly acknowledged in cases decades old.
The Appellate court is the gang that overstepped their authority.
Exactly
This wasn’t a ruling on a state law, however. This was local.