Why are there no faders for the cymbals in the mixer?
The first row of channels in the Addictive Drums mixer controls the sound from the close microphones for each kitpiece. The cymbals in Addictive Drums were not recorded through close microphones, only via Overhead and Room microphones - that's why there is no fader for the cymbals in the mixer.
However - you still have plenty of control over the individual cymbals on the EDIT page. Here's a video on this topic: