I think what you're seeing there are the terrain skirts that CesiumJS adds between terrain tiles to fill in gaps. I'm not sure if there is an easy way to disable it, but if you can provide a Sandcastle example that recreates this we can open a bug report on GitHub to track it.
I think the reason this hasn't come up before is that usually with clipping planes on the globe, the hole is filled with something else (like a photogrammetry model) so those skirts are occluded behind that. Are you doing something similar or do you have a different use case?