ZERO-MAX: The effect of "ZERO-MAX" which Special Summons an "Infernity" monster and the effect which destroys all face-up monsters are not treated as resolving at the same time. Even if there are no monsters on the field, then it is treated as finishing resolving with the destruction of monsters. Thus, even if "ZERO-MAX" does not destroy monsters, then you cannot activate cards like "Torrential Tribute" because you miss the timing.
Junk Collector: If "Junk Collector" is the only monster on the field, then you cannot remove from play "Ceasefire" to activate its effect; if you did, then there would be no monsters on the field after activation, so the damage-inflicting effect cannot be applied. Likewise, if "Junk Collector" is Summoned and is the only monster on the field, then you cannot remove from play "Torrential Tribute" to activate its effect; if you did, then there would be no monsters on the field after activation, so the effect which destroys monsters cannot be applied.
These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
Forced Back: You can activate "Forced Back" when you Normal or Flip Summon your own monster. You should announce this immediately after your Summon. Once you allow your opponent to activate "Torrential Tribute" you are acknowledging that the Summon was successful and you cannot activate "Forced Back".
Gemini monster: When you have a Gemini monster already face-up on the field, you may use your Normal Summon to turn on the effect of the Gemini monster, making it an Effect Monster on the field. This is treated the same as any other Normal Summon, so cards that may be activated in response to a Normal Summon may be activated now, such as “Torrential Tribute” ...
Greenkappa: You can chain to the effect of "Greenkappa", even with the targeted Spell or Trap Cards. If only 1 of the 2 cards is chained, "Greenkappa" will still resolve and destroy the other. If "Greenkappa" is destroyed in a chain to its effect (such as with "Torrential Tribute") its effect still resolves.
Magical Dimension: If your opponent activates "Magical Dimension" and chooses not to destroy a monster on the field, then you can activate "Torrential Tribute"...to destroy the Special Summoned Spellcaster. If your opponent does decide to destroy a monster, then you cannot activate these cards because the last thing to happen was not a monster being Summoned. So you have missed the timing.
Skull Knight #2: If the opponent chains "Torrential Tribute" to the effect of "Skull Knight #2", all monsters will be destroyed (including the Level 5 or higher Fiend-Type monster that was Tribute Summoned) and then "Skull Knight #2" will be Special Summoned from your Deck. If the opponent waits until the effect of "Skull Knight #2" resolves and another copy is Special Summoned, and then activates "Torrential Tribute" in response to that Summon, all the monsters will be destroyed.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.