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:
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!