LAN server with Exim4 in smarthost mode + bsd-mailx: Makes email sent to "someuser" sent to real e-mail address

LAN server with Exim4 in smarthost mode + bsd-mailx: Makes email sent to
"someuser" sent to real e-mail address

My Debian 7.1 box is a private LAN-dedicated server with no intent (for
now) to handle e-mails for public domains and I have troubles with command
line e-mail sending.
I've set up /etc/email-addresses file so that e-mail sent from local users
appears from a valid e-mail address (some SMTP servers refuses e-mails
from non existing domains and it's better anyway):
user: bob452@someemailprovider.ca
root: aliceee@otheremailprovider.de
I can send e-mail from command line with bsd-mailx -s Test jdoe@gmail.com
just fine. However I can't seems to make bsd-mailx -s Test root to work
because I get the following in /var/log/exim4/mainlog:
** root@myhome.lan R=smarthost T=remote_smtp_smarthost: SMTP error from
remote mail server after RCPT TO:: host smtp.myisp.fr [212.1.2.3]: 550
5.1.2 : Recipient address rejected: Domain not found
I need e-mail notifications for monitoring tools/scripts. Some allow a
complete e-mail address, some don't and will send notification to local
user running script (often root).
I read I could use /etc/aliases as follow:
root: jdoe@gmail.com
But it doesn't seems to work: bsd-mailx -s Test root stills tries to send
to root+domain.
I'm using exim4 package v4.80, bsd-mailx package v8.1.2-0.20111106cvs-1.