E.g.: Rex has currently 15 regular Stimpacks in his inventory, Cass has 20. On the Companion Commands screen though it says "0" Stimpacks and I cannot have them healed.

Is this a known bug? Can it be corrected?

The Stimpacks have to be in YOUR inventory, not theirs for you to heal them that way. Otherwise, they will heal on their own.

I see. Thanks. But I still can only use regular Stimpacks on them?