No you don't have to do the rest of the culti's unless you plan to switch from sage to demon, then you need to do every single culti from where you stopped + other things. This means you can buy skills that would otherwise require you to do every culti in order to reach Celestial demon/sage, if you didn't use the fairy, and whatever else requires you to be Celestial Sage/Demon. The Celestial Schism thing, is the thing that allows you to change your culti. It just means that if you one day want to switch culti, you can't just instantly use the celestial schism, it requires you to do every culti on your own. No shortcuts. So unless you plan to change culti, using the Third Sage Fairy was a good thing.
Sorry if this seemed a bit confusing. :l