Let's talk first about the standard rules, then the Master of Shadows variant.
Typically, if a player plays a faction card and if the matching colored die to that card is a zero, that player can give away one of his or her treason cards to another player. That player chooses the targeted opponent but the card is drawn randomly. The treason card passed is chosen randomly (and kept hidden). In our gaming group, we have the player fan out his or her treason cards face down and the targeted player takes one (at random). The card taken is always hidden from other players.
David plays a Noble card (red). The Noble die (i.e. red die) is a zero when David plays his card. That means that David can pass one of his treason cards to another player (David chooses the target opponent and uses the process stated above).
The Master of Shadows uses this same process except that he can give away two cards instead of the standard one card and they can be given to different targets if he chooses.
This can be a very powerful ability so in our gaming group, we do not use the Master of Shadows in a TWO player game.
So it has nothing to do with the dice roll at the beginning of the round. It has to do with playing a card when the matching die is a zero.
I hope this explains it?
Does this trigger when activating a zero-power color matching a building in play, or only on a card player form the hand in a zero-power faction?