I guess this is a fundamental timing question:
The timing diagram in the rules shows that all 4 struggles are in a 'box' that precludes playing card actions or responses.
So, "A Scheme of Byakees" says: "Forced Response: After you win a (T) struggle at a story to which A Scheme of Byakhees is committed, the losing player must either discard a card from his hand, or drive a character he controls insane."
Does the losing player have to act immediately after the Terror Struggle, or in after the success of the last committed story is determined?