Can triggered effects occur even though a creature has summmoning sickness?
You are correct - summoning sickness is not relevant here as it does not prevent a creature's triggered abilities from triggering. It would prevent you from attacking with Aven Wind Mage, or paying costs with the {T} symbol, but you weren't attempting to do those things. See that linked question for the full details.
Another potential confusion in the play here is that it is perfectly acceptable to cast Dramatic Reversal even though it would not directly affect anything. By contrast if you had tried to cast Aerial Assault with no tapped creatures on the battlefield, this would not have be a legal play as that specifies

Destroy target tapped creature.

and you would not have been able to specify a valid target for the spell. The difference here is between an illegal play (one you're not allowed to do) and an ineffective play (one you're allowed to do but doesn't have any real effect).