I don’t know which agency in DHS would be watching ammo sales. I could see BATFE or a Postal Inspector showing up, but none of the DHS components would have any jurisdiction on ammo. The only exception would be USSS if they guy had made threats against the POTUS (or should I say TOTUS.)
It is possible that if he was an legal permanent resident with a somewhat checkered U.S. background that ICE could come calling, but I doubt it.