My dog is on prednisone, will be on it for life, and would die without it. I love pred. I respect pred. I know what pred can do (good and bad). Working at a vets I see it be a maricle drug all the time. I know everyone thinks its overused in the world. It is very hard though when cost is a factor, and the owners just want the itching to go away.
I would say the top side effects are increased thirst, increased urination, and increased appitite. The appitite was the biggest thing for my dog. He eventually adjusted to it, and has been doing very well. Since your dog is on im assuming a high dose, and is not even a week into it yet, then i would too say to just give it time. He will adjust, and the dose Will be lowered (you cant keep a dog too high for too long).
Are the accidents in the same spot each time? Can you lay a bunch of towels down by the door incase he has an accident then he will hopefully go on the towels?
I dont know if i would mess with his potassium/sodium. I honestly dont know if being on pred. you could throw him into an addisons problem by doing that (frequently in addisons you have high potassium/low sodium which is what you are trying to do with the diet).
For now I would just let him have whatever water he wants. Get him outside as often as possible. Feed him smaller meals more frequently, and see how he does. Im glad they found something that works with him! FYI, atopica is Extremely expensive, and takes awhile to take effect (and effect varies with each dog).