Rite of Oblivion exiles your additional cost permanent, does not sacrifice it.
This bug skips dying triggers for you. I noticed this when paying with my Fleshtaker and my Elas didn't trigger.
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Mirro#13439
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DAC169#34537 commented
Did your opponent have out anything that makes their opponent's dying creatures exile instead? Like Etching of Kumano or Misery's Shadow?