The CIA is nominally restricted to foreign intelligence, but edge cases reliably go in the broad-purview direction. US citizens abroad and foreign citizens at home are both fair game, as are US citizens at home who deal with suspicious foreigners, and US citizens at home who are caught up inadvertently in foreign-targeting efforts.

There really is a division of agencies; when it was time to catch the Unabomber, the FBI did all the work on that. But if it deals with anti-government activities or any international connection, foreign surveillance can usually find a legal justification to get involved.