For a while I was thinking TINAS really had a point there, though of course Donald's ruling is the only way to avoid bizarre and undesirable effects. However, remembering my favorite old chestnut of a Dominion timing example cleared things up for me:
1. I play Quarry, Royal Seal, and Talisman.
2. I buy a Mint.
3a. I choose to activate Talisman's when-buy condition before Mint's. I gain another Mint.
4a. I activate Royal Seal's when-gain condition and choose to put the 2nd ("gained") Mint on top of my deck.
5a. Now that Talisman's when-buy effect is fully resolved, I must resolve Mint's when-buy condition and trash all treasures I have in play.
6a. I finally gain the 1st ("bought") Mint. Royal Seal is no longer in play, so I can't use it to top-deck this 1st Mint.
-or-
3b. I choose to activate Mint's when-buy condition before Talisman's. I trash all my treasures from play.
4b. Talisman is no longer in play, so I am not able to trigger its when-buy condition.
In short, when a conditional effect triggers, it and its antecedents are fully resolved before any other simultaneous, conditional effects can be triggered. Secret Chamber in multiplayer is a more mundane example: When an attack is played, the other players go around the table in turn order, each revealing a Secret Chamber and fully resolving it before moving on to the next player's opportunity to reveal and resolve a Secret Chamber. We
don't go around the table and all reveal our Secret Chambers before we start resolving them.
Here's how the current case works, then:
1. Possessed by Alice, Bob has a Trader in hand and would gain a Copper.
2. Possession and Trader both have potential would-gain effects at this moment affecting (at least) Bob, so Alice chooses the order (for Bob).
3a. Alice chooses for Bob to reveal Trader first.
4a. Bob would now gain a Silver instead of a Copper.
5a. Possession's would-gain effect triggers
re the Silver, and Alice gains the Silver instead of Bob.
6a. ...and we're done. Possession's would-gain effect never triggers on the Copper, because now that we're done resolving a different simultaneous event, it's no longer true that Bob would gain a Copper.
-or-
3b. Alice chooses for Bob to resolve Possession's would-gain effect (for the Copper) first.
4b. Alice gains the Copper instead of Bob.
5b. ...and we're done. Having fully resolved one simultaneous event, the other (Bob revealing a Trader) is no longer eligible to trigger.
I
think that's the right way to rules-lawyer this one, anyway!