What puts out the mind

Suppose we call "extinction" (by which I mean nirvana or final nirvana) whatever puts out the wandering mind / mental states. What reasons are there for supposing it does so **after** the mind wanders, not before or during? I suppose (as no sort of authority) saying it does so inside the mind is eternalism, or before - annihilationism. But I'm interested in the question not as a facet of Buddhist doctrine: but the question of whether we "die" in the sense the atheist attaches to death.