Exactly. Except that rather than being a remarkable but rare thing with no apparent causes and no known mechanism, it happens (in this imaginary scenario) every time to revivees.

"Consciousness", after all, is a word we use to name a part of our conceptualisation of mental phenomena, and deductions about the real world made from its definition need not be accurate. It need not even match up to any word in some other human language, let alone the physical result of such a radical operation on the brain as cryonic time-travel.