Apple has a service called "Hide My Email" that helps keep your email private by using a randomly-generated email address directly within a supported third-party app.
If you had registered your milieu account using Apple ID and this feature is enabled in your device, you will still have your emails forwarded to your private email, but milieu will only be able to see and identify you via that randomly-generated Apple email.
For more information, please go to Apple's Support page.