Can a player reveal a Reaction card, such as "Secret Chamber", in response to the Minion action, even if the player who played the Minion chooses the +2$ option?
Yes, you can reveal Secret Chamber in response to Minion no matter what.
Secret Chamber is a Reaction that can be played in response to Attack cards, and Minion is an Attack card. The fact that the person played the card in a way that wasn't "attacky" doesn't change the fact that it is an Attack card.
The same goes for Pirate Ship when using its +$ option. Yes, this makes Secret Chamber an amazing counter against Pirate Ship.
Also, the decision points/micro turn order goes as follows:
Player A plays a Minion.
Player B reveals a Secret Chamber, and then can even grab a Moat from the next 2 cards into your hand, put two other cards on top of your deck, reveal the Moat, and then put the Moat back onto the top of the deck with another use of the same Secret Chamber. See the BGG Dominion FAQ and Isotropic Dominion Server FAQ. In general, you can use a single reaction card as many times as you want.
Note: that B does not yet know if he is forced to discard, and there can be a lot of thinking involved here. If you are forced to discard, you want to take the best 2 cards with you, and leave 5 junky cards for the discard. But if you aren't forced to discard, you don't want to wreck your current turn.
Player A then makes his decision about taking $2 or discarding and taking 4 cards.