If you have taken Binary System Black Hole will deal 50/50 Fire and Cold damage, and will have both a fire and a cold tag.
With only Red Giant taken, Black Hole will only deal fire damage and only has a fire tag.
We have tooltip dps planned for P4 of the Early Access Development Forecast
We don’t know what will be inherented by this, but i guess we get at least some basic informations for a skill by skill basis.