Is this the way it's suppose to work?
Yes, except building the mesh doesn't require a dense point cloud to be built first. Both the dense point cloud and the mesh are derived directly from depth maps.
The quality you specify in the 'build mesh' dialog corresponds to the resolution of the depth maps so, each time you change the quality setting, new depth maps need to be generated at the appropriate resolution.
I would think that once I've generated the dense point cloud any mesh is going to be a derivative of that and a new depth map shouldn't be required.
If you do need/want both dense point cloud and mesh, then the depth maps for one can be reused for the other, but only if you opt to generate both with the same quality setting.
Furthermore, though I think this goes beyond what you're asking, it is possible to keep depth maps for multiple quality levels, but you have to manually right-click the depth maps in the chunk explorer workspace and uncheck the 'Set as default' option so that they will not be overwritten when you generate at a different quality level. Then when it comes to reusing them to build a mesh or point cloud you have to ensure that you have set the appropriate set of depth maps (for the quality you want to 'build' at) to be default before you can opt to reuse them in the build mesh/build point cloud dialog.