I too would love to know if there is a solution for this!

As far as I know, this is how DIGITS works.  The only device that has the outgoing texts, are the devices those texts originated from.  If you sent a text from the DIGITS app, then that will be the only place that text will show.  If you sent a text from your phone, then the only record that sent text will be is on your phone.  

Thanks for the reply and appreciate the explanation.

Just seems odd that T-Mobile couldn't sync up texts.  If I switch texting apps on my phone to another app all in/out texts appear outside of those sent from digits.

That would require major changes to the default texting apps on every T-Mobile phone sold.  That also would open up more potentially for people to access texts that potentially were not sent by them.  T-Mobile doesn’t store the contents of text messages.  That policy would have to change to have the ability to sync messages across devices.  That is why Facebook can do it and why Verizon’s Messaging app can as well.  They store every single message, even after it’s deleted.  

Until about 10 days ago any text I sent from either my phone, or through Digits app on my tablet with my phone's number, would show in my Digits app.

Texts sent from my Digits app only showed in the Digits app thread, and not on the phone.

Now I can not receive any texts on my Digits app, although I can still send through Digits, with my phone's number.