Regarding chains with trigger effects when summoning
Trigger effects cannot chain off of other cards

This is fundamentally a Spell Speed question. Aether, the Evil Empowering Dragon, has a optional trigger effect,1 with the trigger of "When this card is Normal or Special Summoned". As such, it is Spell Speed 1 (the same applies to trigger-like effects, which are the equivalent for spell and trap cards). Spell Speed 1 effects cannot chain off of any other effect (including other Spell Speed 1 effects).

For reference, most Trap cards are Spell Speed 2, with the exception of Counter Trap cards which are classified as Spell Speed 3 (and are the only cards so far with that classification). Therefore, if Aether's effect were to be used, it would activate before your trap card would and resolve after your trap card does (if possible - Torrential Tribute, if not negated, would cause all possible targets of Aether's effect to not be on the field anymore, resulting in it doing nothing regardless of what monster was targeted)

Note that because Aether's effect is an optional trigger effect, it may not necessarily be chain link 1. This would only happen if the summoning player has any other trigger[-like] effects (optional or mandatory) that trigger from a monster being summoned in the same manner that Aether was or if the other player had a mandatory trigger[-like] effect with similar timing.

In those cases (as well as if you have optional trigger[-like] effects with appropriate timings), they all enter the chain simultaneously, Simultaneous Effects Go On Chain (SEGOC) dictates the chain link order for all of those trigger[-like] effects, and then fast effects (spell speed 2 and 3) can be added to the chain as usual. In the context of this question, though, this is mostly irrelevant unless any of those effects have a cost that would prevent the activation of your trap card (including sending it to the graveyard).

1 - These shouldn't be confused with Quick Effects, which can chain off of Spell Speed 2 cards. These have a timing of "during either player's [turn/XXX phase/XXX Step]" and are generally indicated as Quick Effects in the effect text.