I think there’s a difference between magic and a spell.
The Necromancer casts a spell that creates the Undead. But once the Undead is created, that Undead is a magic creature. Like a Demon, or an Elemental. The magic that sustains them comes from the universe itself.
Like, if you were remove the Death Magic from an Undead, they would cease to be. But that’s not a spell that needs to be maintained by a person.