(You mentioned it being a "casual stroll" through the house, do you think it's at all possible he's still getting to know his new home? That maybe he's still "checking it out"?)
From what I understand, Rat Terriers are high-energy-level dogs... 3 miles a day, an hour, may not be enough... Are you like, running all out like "I'm-being-chased-by-Michael-Myers" type of run or is it a casual jog? My dog is a Manchester/ JR Terrier-Mix, and I'll tell you, a two mile walk or slight jog at the park is not anywhere close to enough for this dog... We'll get home and he'll just lay down and look at me as if to ask, "Okay. What's next?"
Do you live in apartment or a home with a yard?
I'm just asking because I know my step-mother has three dogs, one is a pug puppy, and when that puppy gets on the older dogs' nerves she sends them outside and keeps the puppy inside... She keeps an eye on them of course, but she stays inside to occupy the puppy...
Like I mentioned about the stress, it's still a very new environment, he's been tossed from his home to an animal-shelter and now to your home... Possibly more times than just once, depending on what his history is... He could be use to being an "outside" dog, he could be use to being home "alone" all the time, he could be used to being the "only dog"... There's a number of things that he could be used to, and it's going to take time and patience for him to realize that he doesn't have those things anymore...
In the mean-time, I would try to find ways to give him some 'alone-time', either put the others dogs up or out, or put him up or out in an area where it's quiet; Is he crate trained? If not, does he do well alone in a bedroom? I would even go so far as to play soft, relaxing music. (Like classical.) Give him plenty of treats or something to chew on, and let him un-wind for an hour... Do that a few times and see if that improves his behavior, if not, if it makes it worse then you can move on and try something else...
I'm not an expert, but I have a dog that I rescued from the animal-shelter, he's a doll, and I actually used the advice I gave you. : ) It might work for you, too!
Good luck!