Hi Michael! That is a lovely Adenium! Love the caudex! Yeah, it has its own unique appeal that quickly wins you over.
During summer I put my plant in the sunniest area of my garden. It can take all the heat and sun it can take, and it is at that time that I can water it more. But since we do not get a drop of rain here, I can control the watering a bit, just on the root zone and I do my watering early in the day.
Try to add more drainage holes in your container, if you wish to keep it in that container, or if you can find shallow bonsai type containers, those works very well. You can also try to make your media a bit more coarse so it also helps facilitate more draining during rainy days. My plant only got some bulb fertilizer during repot this year and some osmocote in August, got lots of sun and water and it bloomed nicely this year.
Fall is here, the sun still up, the overnights are slowly getting cooler. Watch your overnight temps. If it starts to go below 58F or if your rains are becoming too frequent as the seasons transition to cooler Fall temps, you may want to start preparing it to head indoors, and it will just shed the leaves later, as it goes to sleep for the cold season. I just keep mine dry during the cold season, near a window. When Spring comes it slowly wakes up again, and I bring it out in mid to late Spring, coz sometimes we have some hail as seasons change again. As it is about to wake up you can uproot and check below again, maybe change your soil.
Yes, that caudex can grow bigger..depending on your container..especially during summer. It drinks a lot..very thirsty! Sometimes I think I water more for that caudex. Our area is so dry and very low humidity so it needs all the drink it can get here.