I do not really understand what this review process is. How does it not fall under "advise and consent"?
Because the emperor has declared that it is not a treaty.
It should. But the Corker bill changes the rules. Treaties require the "advise and consent" of the Senate and 67 votes for ratification.
But the Corker bill tacitly accepts that the Iran agreement is not a treaty and, rather than 67 votes to ratify, requires 67 votes to override the President's decision.
Corker bungled the job.