And if it's implicit that you should reveal all discarded cards when they have restrictions on them like that, does that mean that if you discard Tunnels with Opulent Castle you have to gain Gold?
Well no, because there's a difference between "you may reveal this to gain a Gold" and "gain a Gold when this is revealed". In MTG terms, some cards say "Sacrifice [this creature]: [Effect]". You don't get that effect anytime that creature is sacrificed; you only get the effect if you choose to activate that ability, paying the cost of sacrificing the creature.
But you are not quoting the card. My question is because of the actual wording of the card.
The actual wording doesn't change that. No reaction cards have mandatory effects, you have to choose to "activate" that effect. Imagine a card that says "each other player gains a Curse and reveals their hand". Your opponent reveals his hand, which has Watchtower in it. No way is he forced to Topdeck or Trash that Curse just because the Watchtower was revealed. "You may do X to do Y" has never meant "whenever X happens, Y happens".
Tried to think of an example with only real cards where it matters. Closest I can think of is if you discard a single Tunnel. That Tunnel, being on top of your discard pile, is "revealed", but you don't have to choose reveal it and gain a Gold.