Where does the admin mail end up, is that a Gmail address? Im pretty sure that's what hides it, customers sit on all sorts of providers and plain mail() from a fresh VPS gets binned before it hits spam because the box has no reputation.
Super common: You'd have to put WP Mail SMTP on and send through a real mailbox, that fixed it for our shop on TransIP. Not 100% sure it's the same cause for you though.