Hello Han, not sure what caused the browning of your leaf, it may be some insect/bug damage as you said. But usually if I do have to treat a plant with something, I position them in part shade, to dry off. Or do the process before the hot sun hits the plant.
You also mentioned that you just got the plant two days ago, was it growing in a nursery or was it indoors? If it was in some shaded area before, it needs to acclimate to the outdoor heat and direct sun before exposing them head on. Leaves and caudex can get sunburnt, got to acclimate them slowly. Once acclimated it can take all the full sun it wants, but needs stepped up watering.
During summer time I treat my Adeniums like a typical tropical plant, daily watering here in my growing area since it is so hot and dry, we got no summer rainfall here, so it is a long 4 to 5 months very dry season. Temperatures in your area are much hotter than ours, so your plant will appreciate stepped up watering, but do it before the hot sun hits it. This plant is quite a toughie, I have read it can withstand up to 120F, which we have not reached here, so far we got into 112F here during our heat wave the other week.
I do not know what you mean by a training pot, but as long as that container has drainage holes and gritty, well draining media, it should be okay to do daily watering when temps are soaring quite high. It may slow down a bit in doing new leaves like most plants do when it is just excessively hot, but it will certainly keep the caudex rock hard and solid with all the moisture it will get from watering. I don't douse the leaves with water, I concentrate watering on the soil itself and I also spritz the caudex. It is just too dry anyways that in less than a minute the exposed caudex is immediately dry.
It will be different approach if your area is rainy, getting muggy and too humid, then you would need to give some intervals in watering. When Fall season comes around, got to scale down watering as temperatures start to go down. I start hiding my Adenium indoors for overwintering when overnight temps starts hitting 50F.