Why does increasing the exposure of this image in Darktable seem to invert the background?

As paperdigits mentionned, this module works in the LAB color space. That color space works well for some operations, but not everything, and it has some limitations.
That’s why many darktable developers are switching the pipeline to the more generic RGB colors space.
The shadows and highlight module is known to create halos. But this is not an implementation bug. It’s an algorithm bug, in the maths that defines the module behavior. Nothing that a developer can correct. They have to switch to another algorithm.
That’s why the Tone Equializer module should be used for those cases.
To find which are the preferred Darktable 3.0 modules, read the good article by Aurelien Pierre PIXLS.US - Darktable 3:RGB or Lab? Which Modules? Help!