So to be sure I'm doing things right, I log on my server and run
tail -f /var/log/exim/mainlog | grep "myemail@blabla.com"
The i open the admin panel in vB and ask him to send a test e-mail via the diagnostic tools.
But nothing shows on the terminal of the server. The tail process is pending without any output.
I wonder where the chain is broken...
Thank you for your help, Snakes1100 !