Here's the constitutional language: "no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." They got a warrant, specifically describing the specific places (web servers) to be searched and the particular things to be seized. Probable cause is easy, these servers were actively attacking government computers.

I think parent is under the impression that a search warrant is the only kind of warrant. That is not correct.

Why would it not be a valid warrant? The web shells are evidence of a crime.

Also, the typical remedy for a defective warrant is suppression of seized evidence, not criminal prosecution.