If you summon Silent Psychic Wizard, and target, for example Esper Girl for his effect, to banish it, and your opponent chains torrential, then the chain link is:
CL1: Silent Psychic Wizard.
CL2: Torrential Tribute
Resolves backwards: First torrential blows up the field, and then Wizard banishes Esper Girl. You would say, that Wizard couldn't summon anything, because he was destroyed before he banished something. Point of the story is though, that his effect is mandatory, and only cares that he is sent from the field to the graveyard. Which he was. and so he starts a new chain, and summons esper girl after the former chain resolved.