Torrential Tribute is a trap and is a quick effect. This effect is classified as a spell speed 2. Trigger effects like Dark Beckoning Beast, activate first (as they are trigger effects) then once all trigger effects are done being activated, Torrential Tribute will have the ability to activate. Any cards activated in this specific chain (the chain that occurs immediately after a monster is summoned), is considered in response to the summon. To visualize this better, check out the fast effect timing chart:
https://yugioh.fandom.com/wiki/Fast_effect_timingGo to Box A.
When a monster is summoned, it is an action that does not start a chain, so we then proceed to box the blue box on the left.
The yellow box are for effects like Dark Beckoning Beast.
Afterwards, we go to box B and C, all the while following proper chaining procedures in Box D.
In Box D, we resolve the chain, and if after the chain is resolved, there are no more effects to activate, we go back to box A
Hoped this helped!
Sincerely,
DarkPhenix