This is normal behaviour. Mail traditionally worked like this:
- If you want to send a mail to any address, your computer looks up the MX entry for the recipient's domain and send it to this server directly via SMTP. This is regardless of the sender's domain, so you could send mail for any sender address.
- The receiving server handles it and makes it available to the recipient in some way (via file system, POP, IMAP etc.).
So, as you see, it's perfectly normal that your server can send mail directly. However, doing this is not a very good idea today. Because of the massive amounts of spam etc. this once open system got restricted quite a bit.
- Today, servers check from where a mail comes. If you are on a dialup address, many mail servers won't talk to you at all, or classify your mail as spam and throw it away. This is the reason you have to configure your providers SMTP server in your mail client: This one identifies you with username and password and accepts your mails and handles them normally.
- If you are on a server IP address, receiving MX servers will try to decide if you are supposed to send mail for the FROM address you try to drop off. For this they do all kind of checks like including checking the MX, SPF and DKIM records for the domain if available.
Depending on how your domain is configured, many receiving mail servers might decide that your server is not allowed to send mails for your domain and disregard it. To prevent this you have to do one of the following:
- Send mail with the Google Apps mail server as relay. For this you have to configure your local mail system (Postfix?) to use this relay.
- Configure your DNS domains with at least SPF records that includes either all servers or Googles and your own and configure your local postfix as good as possible (you will find many questions about how to do this on SF).