Is that really their job? It seems there might be a dozen other agencies responsible, ones less interested in foreign computer networks. Is that DISA's bailiwick? Perhaps NIST? Homeland Security? et cetera
Information assurance. Products and services for government and businesses.
The agency that deals with intelligence (espionage) is the CIA, and the CIA do have their own cyber espionage systems, NSA not only is not doing their actual job, but they are being redundant.
Which is fine, of course, but why are you trying to speak as if you have authoritative knowledge?
You say that NSA is responsible for cybersecurity within an HR agency because their name has "SECURITY" in it, and as far as I can tell this is meant completely seriously. So should NSA also be responsible for the military defense of the nation since their name has "SECURITY" in it? Should they regulate financial markets because their name has "SECURITY" in it?
In case you wish to know, NSA is responsible for (among other things) 'SIGINT' and 'ELINT'. CIA is responsible for 'HUMINT', 'OSINT', and many other fun things.
Both the NSA and CIA are foreign intelligence agencies, mostly due to historical accident. And of course there's an entirely separate DIA, which also exists mostly due to historical accident, but focuses mainly on military intelligence matters.