The mail sent by your server’s cron jobs are refused by the recipient server due to:
"Action: failed Final-Recipient: user;user@domain.com Status: 5.0.0 Remote-MTA: dns; inbound.smtp.domain.com Diagnostic-Code: smtp; 553 5.1.8 ... Domain of sender address root@hostname.domain.com does not exist"
Crontab will by default send from $LINUX_USER@$HOSTNAME. You can change this by connecting to the server via SSH, running “crontab -e”, and adding “MAILFROM=VALID_ADDRESS_HERE”. Ideally, the MAILFROM will be set to a mail account hosted on your server, but if it is a valid domain, the recipient address will accept it.