Show: All formats Goat Perfect Circle Edison
"Torrential Tribute" is activated after a monster is Summoned; it is not chained to the Summon. So you cannot activate "Torrential Tribute" when "Jinzo" is Summoned.
Like most Trap cards, this card can miss the timing. For example, if "Jar of Greed" was activated, and "Call of the Haunted" is chained to it, this card cannot be activated when that monster was Summoned, as the Summon was not the last thing to happen (Jar of Greed drawing a card was). You can read more about Timing here: https://www.mikamika.de/edison-rules
"Torrential Tribute" can be activated after a monster is Summoned through another card's effect, such as "Monster Reborn", "Scapegoat", "Cyber Jar" (if Flip Summoned), or "Call of the Haunted".
"Torrential Tribute" can be activated after a Flip Summon, but it does not negate the Flip Effect (it is chained to the Flip Effect).
"Torrential Tribute" cannot be activated during the Damage Step. This prohibits "Torrential Tribute" from being used against monsters Special Summoned by "Mystic Tomato", "Giant Rat", "Nimble Momonga", "Masked Dragon", and other such cards that Special Summon a monster when destroyed as a result of battle, as well as "Cyber Jar" or "Morphing Jar #2" that is flipped face-up by an attack.