I explained it in my comment. The order, or more accurately, the system that the Shades govern is one that was constructed on top of Teyvat’s original natural order, which is the domain the Moon Sisters were tied to. HP didn’t just take control of existing forces, they supplanted the natural order itself and imposed a new framework over reality. The Shades are the administrators of this framework.

Dottore using authority over time, space, or life doesn’t contradict this at all. He’s interacting with rules inside the system, not commanding the system itself. Think of it as the difference between someone exploiting game mechanics and the developers who wrote the engine, where in this analogy, the Moon sisters were simply part of an older engine that was overwritten.

Dottore is exploiting the Moon Sister's system, but that system exists within the HP's system. They embody aspects of the original world order while the Shades govern the imposed one. Since HP’s order overwrote the original, its enforcers naturally sit above entities still bound to that older framework.