Jurisdiction is generally where the crime was committed. Yes, there are federal prosecuting attorneys in SDNY, and every other jurisdiction in the US.
-- Will Mueller get to poke through Cohen's stuff? Or are the people of SDNY doing it? --
This raid and any fruit from it could go back to Mueller, depedning on what is found. If the material is election campaign related, back to Mueller it goes.
This could well be a coordinated fishing expedition, where Mueller wants to appear to have clean hands in case nothing turns up.
Exactly. Well stated.