As visible on the second screen shot, it didn't discard cards from my hand. (There is no card left of the stripe indicating whose cards are discarded.)
Furthermore I just might formulate it as: Witcher counts all "New Cards" regardless weither it's the case it's just the card drawn after Witcher or if it's discarded by it.
Besides, the effect of a card always happens before the new card is drawn, else there would be a chance Battle Formation gives 32 attack and 15 wall even when you currently have 3 Soldiers on hand, if you happen to be lucky enough to draw a soldier after that.