Multibounce lighting is achieved by voxelizing all geometry and adding indirect lighting from the previous frame to direct lighting. So, it only works correctly when you voxelize all geometry on every frame, and each frame adds a bounce. If you make incremental updates, there will be noticeable changes in lighting: some areas will have more bounces than others. And by areas I mean axis-aligned boxes in voxel space, so there will be sharp boundaries between areas updated more or fewer times.
Not every camera movement requires updates. The reason why updates are required at all is that the voxel clip-map covers a limited range of world space. When you move the camera (or rather, the anchor point which is normally somewhere in front of the camera) enough to change the position of the clip-map, regions in world space that were not covered before will need to be filled by voxelization. Moreover, there are multiple levels of detail in the clip-map, each covering a different range of world space, and they move together, so a single change in clip-map position triggers updates to all the levels.