I have 2 accounts - account 1 is a hotmail account and account 2 is a Gmail account. I have used the standard setup to setup these addresses on my app.
All emails received in account 1 automatically appear in account 2 inbox, so I receive 2x notification for the same email. If i delete the unwanted email in account 2, it deletes it from account 1 also.
It does not happen the other way around - emails I receive in account 2 do not appear in account 1.
Forgive me, I'm reluctant to post screenshots of my email accounts online.