couple of things you could try.
What is your email address? I will send you a question, and if you reply back then I will know this email address exists and your setup with postfix is fully functional. It will be a real world test, and no one will know what the question is-- only the sender, and its recipient. Give a different answer, and maybe someone else is trying to reach you at the same time, which may not be a bad thing.
After adding those lines in .bashrc, did you source it? Source it with this command (for the sake of anyone reading this) ". ~/.bashrc" without the double quotes. And yes, that is a dot followed by a space.
And I will only ask this once: Must it be root?
Well ...... I did not undestood what do you mean .....
I will explain more in details and give some other clues
I found in internet a script to put in .bashrc that alert me with an email when someone login ( as root or as user )
I put the script in root's .bashrc and user's .bashrc.The email for both login are now sent to my user mbox.
The script works because the email arrives but I was waiting during my terminal works the messagge
"You have new mail"
but for those email this does not happens.
Tried to send a test email from root to my username and: the email arrives too and in this case
I have the terminal notification