Rules Question: Psychic Attack and Inv and/or cover saves

Quick question from a self-confessed noob.
Typhus psychically attacks a squad of terminators with Wind of Chaos. Typhus auto passes, so all terminators touched by the template should take a wound on a 4+. Here's the question: Do the Terminators in this instance get their Invulnerable save? Would other models get a cover save if applicable? We weren't certain based on these two lines of reasoning:

No saves of any sort: a psychic attack should bypass armor as it is not really operating in the physical realm.
Yes, they get the saves: it is a psychic "shooting" attack and Invulnerable rules were designed for just this kind of thing.

Any thoughts from more experienced players?

The rules for Wind of Chaos say no armor or cover saves, BUT, don't say "no invulnerable". They get the invuln.

If it was Mind War, they'd get cover saves also (per the Eldar FAQ iirc).

Correct.