Twilio evangelist here.
First of all please note that the SmsMessages resource has been deprecated and you should now be using the new Messages endpoint. You can check out the Sending SMS Messages quickstart for updated Java code that shows how to use the new resource with the Java helper library.
Second, in order to receive notifications as a Messages status changes you should include the StatusCallback parameter when you send the Message. Including this parameter tells Twilio to make a request to the parameters URL when the message status changes.
Also note since its not clear from your post title, the "sent" status simple means that Twilio successfully sent the message to the carrier. It does not necessarily mean that the carrier was able to deliver the message to the intended recipient.
Hope that helps.