Predinose is powerful stuff. It's quite possible that the higher dose is still affecting Jasper. Pred stays in their system a long time and even the lower dose is still going to make him ravenously thristy.

My Sleet used to take Pred for her allergies. I found she had to go outside at least every 3 hours or she would have accidents. Sleet is a dog who regularly goes up to 16 hours without asking to go out. Sleet takes a different steriod now as I couldn't stand some of the other side effects of pred. It doesn't work quite as well, but she doesn't turn into a demon dog on it and the itching still stops.