What you've got there is more commonly known as an Usambara baboon, it's a Pterinochilus species, more or less officially believed to be a colour variant of P. murinus (although some insist it is a different species or a subspecies of P. murinus). It is an arid climate terrestrial with some tendency to show semi-arboreal behaviours.
Keep it dry with just a water dish, no misting, in a terrestrial habitat. They're heavy webbers so any climbing desires it has will be met by navigating its many layered silk tunnels and hammocks.
I keep mine in a habitat that has vermiculite on the bottom with a hideaway that it can live in and plenty of wallspace and roofspace to crawl around on. It makes lots of web hammocks and tubes and is a really cool spider.
Mine has a deep substrate of peat moss and potting soil with a piece of sandblasted driftwood angled across the cage. She spends most of her time in the burrow she excavated, but does come out at night to hunt and spends a lot of time then perched on the driftwood.
I think part of the confusion comes from the fact that some of the other T's that carry common names like "sunburst" and "starburst" are aboreal, such as Heteroscroda maculata. The words "Sunburst", "starburst" and "Baboon" tend to turn up the common names of many african tarantulas and are used interchangably by dealers.
Furthur confusing the issue is the fact that they climb nearly as well as an aboreal. These things can move! Their climbing abillity, added to the fact that they web so much it acts like a safety net, it's been suggested that the hight restrictions normally recomended fot terrestrials doesn't really apply to them. I still keep mine in low containers, however.