Well the answer is -- it depends. For most people, the rash will show up up to 8 hours after. Off the top of my head, I believe the averages were 2 to 8 hours after contact. For the first time ever reaction, it could even be the next day.
Spreading really depends on a number of factors. Could there be re-infections occurring -- meaning that the person is still coming in contact with urushiol oil. What part of the body did the urushiol oil come in contact with? Thinner skin areas such as the inside of the elbow will generally show a rash long before thicker areas like the outside of the elbow, knees, etc. It is extremely difficult to get a rash on the soles of the feet due to the thickness of the skin. Could the home treatments be causing a secondary rash? So.. probably a day or so.
If your husband did not come in contact with the plants, then yes, it is likely that he picked up the urushiol oil from your dog. Secondary sources are very common -- and probably pets are at the top of that list.
Whenever my dog goes through the woods, I have him jump in the pool. That helps to remove the urushiol oil. Even a good hosing will help remove at least some of the urushiol oil though using soap is the best.
Hope this helps.