cricenog thank you for participating in the beta. This will be a lot easier to find for other beta users with the same question or concern.
At this time, the messages sent from the DIGITS webportal and stand alone pc client will not show up in the native client. You still have the option to install the DIGITS client on your phone, this way you see the messages there.
This is a hot topic so we are currently working with device OEMs to combine DIGITS into the native clients.