I don't think we have that kind of clay here (and we do have a basement that has had no issues), and our builder has been putting up houses in this area for a long time, so I'm sure he'd be aware of the problem if it existed. He says there will be a 3 ft deep footer around the perimeter. He doesn't think the tree roots will be a problem, and of course a lot of them will be dug out when they dig down for the footer. Come to think of it, there used to be another of that same type of tree closer to the house; you can see where the stump used to be, and it's demise hasn't appeared to impact the house at all. I'd forgotten about that.
They're supposed to start construction around the first of April, so soon!!