If Apple ID address and password is same as web mail account and the mail application is configured with it ( set as IMAP account ) an immediate mail is received in inbox both in web account and imap account that you signed in with the Apple ID .
Note : it has nothing to do with clear all history and web site data or say if you were using private browsing even the mail will be received .
Also , you must have set up different devices like Mac / iPhone with your browser from where the Apple ID is signed in .
If you sign out all browsers the different devices will be disconnected from your primary browser .
The mail is received on the browser from where Apple ID is signed in and not on other browsers .