The contractor at my neighbors house was washing out his brushes with turpentine or paint thinner and dumping the liquid right next to my tree. Is my tree going to die? What can I do to help it survive?
Paint thinner won't really hurt an established tree, as long as you don't make a habit of dumping it underneath them. If the tree is small, say 3" or less in diameter, it might cause temporary shock due to water displacement in the soil. After a rain you should be fine.
Unless your tree is growing in contained soil, such as a planter or curb box. If that's the case, remove as much of the contaminated soil as you can without damaging the structural root system, and replace it with fresh topsoil.
Personally, I would ask the contractor to use a different dumping spot, in the future.