Ich looks like grains of salt. Try to refrain from medicating an animal unless you are positive of the problem it needs to be treated for. Meds are stressful so it's best to try to go without having to. Did the puffer have ich? Were there any new fish put in the tank recently? What other fish live with the puffer? You said the water seems fine. When was the last test done and what were the results?
For right now, he can go back into the hospital tank, but don't medicate with copper. Just simply make sure the temp is stable and maybe add a little garlic in the tank. Kent Marine and Seachem make garlic additives. You can also give him a dip for three minutes in temp appropriate dechlorinated freshwater. I'd like to know the results of each test...ammonia, nitrite, nitrate, pH and specific gravity.