The behaviour currently is:
1. Open Twitter app, find a tweet with link to an interesting article.
2. Long press the tweet to open the "context menu".
3. Choose "Share via..." to open the system share intent target chooser.
4. Choose "Add to Pocket".. obviously :)
5. Go to Pocket to find that the tweet was saved on the list not the article linked in the tweet.
6, 7, ... some additional steps to add the actual article to the list and remove the tweet.
In the 5th point above I expect to find the article linked in the tweet on the list (with tweet metadata saved with it and appearing as the grey bottom bar after opening the article). This is how I remember it working just a few days ago.
Unfortunately I am not sure if the problem is on your side or Twitter's - I remember both apps updating recently.
Pocket 188.8.131.52/Android 5.1/Moto X (2013/1st gen.)