The Beauty pass is always unaffected by LightMix, that is correct behaviour :) Only the LightMix pass is affected by LightMix.
When you bake to scene, you need to re-render again to see the changes (which now will show in the Beauty pass since the lights themselves have had their values adjusted). I did a quick test and increased a CoronaSun in LightMix to 10 from 1, used the >Scene, re-rendered, and Beauty pass correctly showed the Sun now 10 times brighter.
Can you provide more information on what you are experiencing? Are the results you describe after re-rendering? Is it only for certain light types?