How to properly pigtail a second light source from existing light switch
It sounds like you connected the dimmer to the fan speed control output.  Don't do that. 

In fact, just go ahead and bypass the dimmer and wire it cable B neutral to neutral bundle and cable B black to the bundle you think is "always-hot". This will make the light go on 24x7.   Then, operate the fan speed control and see if the lights are affected, If they are, you got the wrong black bundle. Switch.   

Once you're sure of the black wire, then install the dimmer.