Pretty certain TINAS has it correct, and dondon, the order actually is explicit (I had to check it): discard, then draw. So, if you currently have:
Watchtower, Tunnel, Copper, Copper, Silver
and your opponent plays a Minion, the order is:
Discard the Tunnel
Reveal the Tunnel (as it is discarded) and gain a Gold
Reveal the Watchtower and place the Gold on your deck
Discard the Watchtower and coins
Draw Gold and 3 more cards.
Donald's indicated that things that are called for at the same time "happen" at the same time. The reveal of the Tunnel must happen as it is discarded, which means it happens at the same time. The gain of the Gold happens at the same time, as does the reveal of the Watchtower. This all happens while cards are being discarded.
It's implicit but not explicit that, much like playing coins during the Buy phase or discarding played actions during the cleanup phase, discarding cards has an order to it. In other words, you could discard the Watchtower first, and you would lose the ability to reveal it. Since this sort of situation applies, I think, only to Tunnel, you'll always want to discard Tunnel first, much like you always want to play Contraband first during the Buy phase, and clean up Alchemist before Herbalist during the cleanup phase (if a Potion is available to clean up).