Gabe, They can all be outside and will grow best outside as long as temperatures are above 60F.
I see that you are in S. Arizona. A few acquaintances from Arizona have theirs outside all year round. If temperatures at night get low, then they have in greenhouse or bring inside. Often they have to keep theirs during the extremely hot weather they have to have them under shade cloth or close to trees that will give filtered sunlight during the hottest hours of the the day.
They can take high temperatures, but with good humidity. If it is dry heat, then better in filtered sunlight. Also, their watering needs will have to be increased if they dry out within a day or so.
If you plants have been out of direct sunlight, then make sure to slowly introduce them to the sunlight. The leaves will and can burn if left out too long when not acclimatized to the sunlight. The Caudex (the trunk/girth) of the plants can also burn if not acclimatized.
Your Fatguy looks fine and the sap may have been from the leaves broken off, but it will regrow new leaves. Looks as thought it is in a dormant state right now, that is why it has not leaves.
The A. swazicums are beautiful and have exceptionally nice single blooms.
Rick