As a reaction card, Watchtower can be revealed whenever you gain a card.
Does this apply to the card you receive from other players during a Masquerade?
No. A passed card is not considered a gained card.
From the Intrigue rulebook:
“Pass” – when a player passes a card to another player, he places that card face down on the table between himself and the other player. The receiving player then takes the card from the table and puts it in his hand. A passed card is not revealed to the other players. A passed card is not considered to be trashed or discarded by the player passing it and it is not considered to be gained by the player receiving it.
The only way you gain a card is if the card specifically says the word "gain" or when you spend money to buy it off of a supply pile. Anything else that results in you having a new card in your deck is not a "gain".
Edit: Total brain fart, thanks commenters!