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Warptime allows a unit to move as if it were the movement phase.

If I cast Warptime on a Rhino, does that mean the occupants can disembark? Disembarking is part of the movement phase.

Normally I would say no, this is a separate unit and psychic abilities don't affect occupants. But there's this distinction between on-the-battlefield / off-the-battlefield with units in transports that's made it's way into the game. Occupants of a vehicle are treated as part of a unit with the transport for the purpose of measuring drops, and as being on the battlefield for the purpose of determining PLs for deep strike.

While I would not argue that unit should be able to further benefit from the Warptime power once they have disembarked, I'm wondering if occupants are wholly separate from the transport while they are embarked. For the purposes of carrying out this special movement phase, shouldn't the occupants of a transport be able to do what they normally would do?

Disembarking is an action of the embarked unit, not the transport. For them it's still the Psychic phase.

You can’t cast Warptime on the unit within, and casting it on the Rhino wouldn’t affect the occupants.

 Ghaz wrote:
Disembarking is an action of the embarked unit, not the transport. For them it's still the Psychic phase.

This. You're affecting the transport, not the unit inside.