Apropos of nothing, I believe I've figured out what the Cai White Rooms do. The hint is actually in the name itself, which makes the answer a little bit meta knowledge, a little bit pun.
Simply put, they're isolation rooms. The provide an environment to cultivate in that's clean from interfering energies. This includes higher energies, not just qi. Higher realm cultivators are able to explore and refine their Way/shen/pearls/etc without having to account for distraction and disruption from outside forces.
It's even conceivable the artificial environment provides a measure of insulation against some of the fundamental laws of the modern world, offering a more fluid environment, more akin a younger material realm less cluttered and stifling with Laws. Block off the right threads of reality, and progress might simply be more, well, simple.
This theory, overall not the stretch possibility immediately above, is substantiated by the qi blanching effects of certain Cai techniques we've witnessed. Renxiang's blasted material into an odd quasi-unreactive qi state, and the state was reasonably persistent. Meaning the Cai have techniques for manipulating the energy state of an area, in an at least somewhat lasting manner. This demonstrates the means to create energy isolation chambers, in broad terms.