You are lucky, at least in my opinion. I have wanted one of the obesumxswazicum for some time.
Where was the plant situated at B&B cactus when you bought it (sun or shade)?
I am not all that familiar with the weather, temps. in Arizona, but if you have Adeniums already, you should be able to treat this one the same.
If the plant was not acclimatized to full sun, the caudex could get sun burn.
This O x S that you have are supposed to have a longer blooming season
than many others. If the plant is going dormant, there is not much you can do. Could be triggered by cold or drought.
Many of the Adeniums can stay semi-evergreen/evergreen depending on the conditions.
In the winter many both swazicum and obesum go dormant for a short time.
If it is not growing and the temperatures are low, then reducing watering.
If you bring in the other Adeniums at some point. I would do so with this one then.
Rick

It was sitting in the middle of the greenhouse. Most of the Adeniums in the greenhouse seemed to be losing their leaves while some had plenty of leaves. I think it has to do with drought because I repotted my O x S today and the soil was bone dry and The temps in Tucson are about 5 degrees F hotter than where I am. B&B are probably treating the DR's as if it were winter because about a month ago when I was there all the DR's were outside (including the one I got) and many of the DR's in the greenhouse were full of leaves. So if I just give it a little bit of water at a time would my O x S simply come out of dormancy until temps get cold?
I also just realized my other DR is an Obesum x Swazicum as well... over a month later lol

I would water it moderately because if it has gone dormant it will not be taking up water. Water sparingly until you see new growth starting.
They may have just stopped watering them as it was getting cooler night time temps. outside and moved into greenhouse. They would go dormant in winter anyhow.