I suppose the issue is in part with an ambiguity in the meaning of "if two things happen at the same time, the player orders them", as it applies to reactions. One possible interpretation (which isn't the correct one) is analogous to the case with, for instance, playing a Pawn. For instance, when you play a Pawn, you can't say "I'll take +1 card, now I draw my card; okay, and for the other half of the Pawn I'll take +1 action"; you have to decide which two effects of the Pawn to take before you resolve either of them. One might think that, with "two things happening at the same time", the player would have to choose the order in which to activate them before doing either: "Ah! You've played a Militia; I'll reveal Secret Chamber and Horse Traders, activate the Horse Traders first, and then the Secret Chamber." Under this scenario, if you draw another reaction from the Secret Chamber, it's too late to reveal it as well.
Again, I'm not arguing that this is the rule of the game; it's not. I'm just arguing that the printed rules (excluding card FAQs) and card texts don't clearly distinguish between the correct and incorrect interpretations.