I can’t tell if the cron job is running on your system. Maybe there’s a protocol where you see this?
On my EGw/Debian that is written to syslog:
May 20 21:10:01 egw05 CRON[24121]: (www-data) CMD (/usr/bin/php -q /usr/share/egroupware/api/asyncwrapper.php)
The executing user must of course also have the right to execute the script. For me on ubuntu/nginx this is the user www-data. The same user as the web-server-user.
If this is done correctly, a smpt-only-mail account must also be created. No user is logged in to send the notification…
And always: look into the protocols of the servers…!
Greetings
Stefan