This ability is used after the event's effect resolves (or is cancelled) and the card is placed into the discard pile. It shares the timing window with any Reactions to the effects of the event (e.g. your opponent plays Put to the Sword and kills your character, you trigger Tower of the Sun (reaction to an event being played), gain 1 gold and use it to play As Hard as Winter (reaction to your character being killed).
The cost of an event is paid, and the effect is resolved, then you can trigger Tower of the Sun as a reaction to the event being played. So youcannot play and event, trigger Tower of the Sun, and then use the gold you gained to pay the cost of the event.
Furthermore, when your opponent plays an event, and you want to cancel it with Hand's Judgment, HJ is an Interrupt, so it comes before Tower of the Sun's Reaction. Therefore, you won't have the gold from Tower of the Sun yet to pay for a Hand's Judgment.