Rich is on the right track. If you build them while you are in the humid cycle, then the gaps will grow. Generally, a call back on the too large gaps does not require any work from your people other than you arriving with a few calculations from the Shrinkulator.
You have consulted the Shrinkulator, right?
If you live in the Midwest, the Oak doors will sit at about 7%-9% in a house with 30% RH. If your lumber is 6% upon arrival at your shop, and close to that when shipped, then a 30" wide flatsawn door will expand to just over 30-1/4". If quartersawn, then it will expand to just over 30-1/8".
Prior to building, I would walk them thru this with a nice simple example, explaining that this is science - neither voodoo or guesswork or opinion. Give them a 12" long pice of Red Oak, and show them how they can blow bubbles in a glass of water.
Then ask them if they will let you do what you would do as a professional, or would they prefer tight gaps, and likely problems, with numerous callbacks, ending up with what you suggest today - allowance for the material's properties.
And the cleats on the back? Again, Rich is right that they must be slotted screw holes, with washers under the screwheads. And the slot sizes? Just a hole in the center of the cleat's length, with the slot length increasing as you move out to the ends. The Shrinkulator will help you determine the slot length.