I would suggest running the heat (UTH) set to the required temperatures for several days at least (a week is preferred) before your snake moves in to make sure it's neither too hot nor too cool for your new BP. It can take a few days for UTH to build up heat (it gets absorbed by surroundings- what the tub is sitting on, etc), so if you rush this, & aren't paying attention, it can get too warm. (I know you'll be "paying attention", but just saying...)
I wouldn't worry about what the t-stat says- you need to set it to whatever temperature achieves the warmth you need inside the tube, where the snake will be touching the substrate over the UTH. You don't want that over 90*, but it's fine if it takes setting the t-stat over 90* to achieve that. Obviously you're measuring inside the tub independently, not taking the t-stat's "word" for it.
Also- remember that we're 98.6* roughly, & that's why 90* feels "cool" to us.It confuses most everyone at first, lol. But you seem to be on track- the only other thing that might help is putting dark paper on several (or 3) of the sides to add privacy for the new snake- otherwise your movements nearby will likely scare & stress the snake. Some just put a towel over half of an enclosure instead, which is fine too- as long as there's no heat-generating light on top & next to flammable fabric.
Remember that snakes see motion well, but don't identify us visually- so anything moving nearby is either prey or a predator to them. And new homes are already unsettling & stressful, so privacy can help them settle in, & eat sooner for you, too.
It looks like you have quite a few ventilation holes- if you have trouble maintaining heat & humidity, you might find yourself covering up some of them (from the outside only, with tape)- that's another reason to test this out before the snake moves in.
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