The opponent chooses whether to exile cards from the top of their library until they exile a nonland card or to exile the top four cards of their library. They don't choose whether you cast the cards exiled by the first option.

When a player faces a villainous choice, they first choose one of the two options, then all actions in the chosen option are performed.

If a spell or ability requires multiple players to face a villainous choice, the result is a little different from other effects in Magic. In that case, the first player in turn order makes their choice and the action for that choice is performed before the next player makes their choice. Then each of the remaining players repeat this process in turn order.

A player facing a villainous choice can always choose either option, even if one or both of the options are impossible. For example, if one of the options is to sacrifice a creature, a player who controls no creatures can still choose that option.