As an expert in external shoulder rotation
(because my arm is addicted to doing it when I throw - I didn't ask for it) I contend that tips like "pour the coffee" are more useful for some people than others. I think some people need to do it more than others to get the disc in an optimal position by the time the disc is released.
The thing to keep in mind is that you rotate your wrist due to muscular action (brachioradialis for supination and pronator teres for pronation) at the elbow, and you rotate your upper arm due to a similar action (supraspinatus for internal rotation and infraspinatus for external rotation) at the shoulder. Supination of the wrist can occur because of either, or both. The muscles in the wrist and elbow cause direct wrist rotation, and the ones in the upper arm and shoulder cause indirect wrist rotation (because the entire arm rotates).
These problems always originate upstream. You just have to figure out where the rotation is coming from. The "pour the coffee" action is more related to the wrist action, and uses a lot of the muscles there (more than described above) because it's a somewhat complex movement to get you to position the disc properly. You need to have the right grip, and ensure the rest of the arm is positioned properly. That's where upper arm rotation at the shoulder can complicate things.
I think it's better to just post a form check for review here, and let the brilliant people here tell you what's wrong. I think it's super easy to misdiagnose some of these problems (having done so myself) but targeted advice can go far.