During the Summon response window, due to Fast Effect Timing, first the turn player must activate any compulsory effects that they triggered, such as "Summoning Curse" and "Summoner Monk", then their opponent must do the same. Then, the turn player has the opportunity to activate optional effects like "Torrential Tribute" and "Armageddon Knight"; if the turn player passes, then the opponent also has the opportunity to activate these effects. If at any point either player starts a Chain, standard Chain rules are followed.
This window will open even if a monster is Summoned by a card effect rather than as an inherent Summon. However, this timing will be missed if a monster(s) are Summoned by a card effect that is Chain Link 2 or higher, unless the activation of all other cards and effects that would resolve after it are negated. Also, if the card effect that Special Summoned the monster(s) did something else immediately after Special Summoning the monster (e.g. "Magical Dimension"), then this timing will be missed.
Unlike the Summon negation window, cards that do not specifically respond to the Summon can still be activated (as long as their timing is correct). Also, cards that respond to the Summon specifically can be activated in later Chain Links, since they are responding to the action and not negating it.
During this window, the monster(s) have already been successfully Summoned, so are on the field. If the Summoned monster(s) have Continuous Effects, these are now active. If monster(s) that were just Summoned are moved to a different location during this window, they are considered to have left the field (unless returned to the Main Deck).
Furthermore, if the card effect that Special Summoned the monster did something else immediately after Special Summoning the monster (e.g. "Magical Dimension", "Drill Warrior", "Telekinetic Power Well", "Trojan Gladiator Beast", etc.), then this window does not occur and any cards that can be activated in response to a Summon miss the timing.
The turn player attempts to Summon "Black Luster Soldier - Envoy of the Beginning", banishing 1 DARK and 1 LIGHT monster from his/her Graveyard. The Summon negation window is opened and both players pass, so the Summon negation window is closed and "Black Luster Soldier - Envoy of the Beginning" is successfully Summoned.
The Summon response window is open now, and the turn player can activate cards in response to the Summon of a monster. If the turn player passes doing so, then the opponent has the opportunity to do the same.
If either player activates "Torrential Tribute", "Black Luster Soldier - Envoy of the Beginning" (and all other monsters of the field) will be destroyed. Even though "Black Luster Soldier - Envoy of the Beginning" is destroyed, its Summon was not negated, so it was successfully Summoned. As such, it can be Special Summoned by a card like "Monster Reborn" later.
If both players pass without responding to the Summon, nothing will happen to "Black Luster Soldier - Envoy of the Beginning", and the "Summon response window" is closed.
There is only one Chain in the "Summon response window". After that, no card or effect can be activated in response to the Summon.