Dualists tend to have the intuition that it's an absolute quality--or at least, something with a special status beyond a higher-order description of patterns in physical activity. Your turbulence example is perfect: I can't imagine a fishtank that is atom-for-atom identical to a system that's experiencing turbulence, but somehow isn't "really" turbulent. I can easily imagine a system that is in the exact same state as my brain, but isn't having any internal experiences.

In Philosophy of Mind, this is discussed in terms of different types of "supervenience" and whether the mind supervenes on the physical world in the same way as something like turbulence or digestion, or in a more limited sense where the physical world determines the content of experience but there's still more going on; and I think some say it doesn't supervene in any sense at all (but that probably just comes down to a disagreement about terminology).

Physicalists say consciousness supervenes on physical processes in the exact same way as higher-order physical properties like turbulence, digestion, being alive, etc. Dualists feel that still leaves something out.

But if it's an absolute quality, it shouldn't depend on the arrangement or state of brain matter at all. The mass of a group of atoms is an absolute quality that doesn't change depending on how you move them about. Yet our experience of consciousness depends totally and critically in highly testable ways on the arrangement of atoms in our neurons. There doesn't seem to be much absolute about it at all. Even tiny changes can eliminate it completely. I just find it very hard to credit the absolute quality proposition, yet I don't see how dualism can avoid it.

So yes materialist answers to this question still have a lot of explaining to do, but dualism can't have a free ride either. It certainly doesn't seem to me to be simpler. At least in the physicalist explanation we can point to other epiphenomena and compare them to consciousness in broad ways. But what known, explicable, testable phenomena can we compare dualism to? It stands apart from all of science.