Are orders issued from one unit automatically rescinded when you transfer to another National Guard unit or role?

How can a unit order you to do something if you are no longer in that unit?

They aren't auto rescinded. A submission request to cancel orders has to be submitted. If you know for a fact that you will no longer be assigned to the unit that issued the orders prior to the start date of said orders, give your unit the heads up so they can get them cancelled.

First of all, nothing is "automatic" in the Army.
It's the Army, not Skynet.
Anything that needs to be done has to be done by two or more people.
If you haven't learned that on the way to E6, at least know it now, and make sure your Soldiers never assume that anything is "automatic".

If those orders are for AT or something else at your previous unit that you will not do, your previous Readiness NCO needs to go into DAMPS and submit a revoke, someone at BDE and/or G3 needs to review it and approve the revoke.
If those orders are for a school reservation, you need to provide a copy to your new unit, the Readiness NCO needs to submit them for pay, and a milpay tech at your USPFO certifies that so someone at DFAS can pay you.

If these orders are for an ALC reservation, you really need to go.