What's interesting is that they logged into my webmail to create rules to forward all mail from Delta to trash so that I wouldn't see any of the notifications.
If email isn't your only method of contacting your customer... then sending an email to an address controlled by a hacker isn't your only option.
That's obviously false. The context of this very discussion is that more than one person is able to log into an account for many email accounts.
In terms of notifying them, I think an email would be appropriate, although straight up saying that the customer's account has been compromised might not be the best idea because the hacker could update their software to look for that. It might be better to send an email about some billing issue, and when the customer calls then explain to them that their account has been comprimised.
I often wonder why Gmail 'Suspicious login' emails aren't like this.
The user could also get the email on their device if the hacker doesn't delete it quickly, which is a possibility given the low and slow nature of this scheme.