Having choosen which clan to activate the phasing player rolls two dice and cross references the result on his clan table. This shows whether the activation attempt for this clan has been sucessful or not. You can only attempt to activate a clan once per turn and, pass or fail, a CP has been spent. Once a clan is activated another die roll may be necessary to determine which side it enters the battle on. This roll can be modified by how the battle is going at that time and the status of other clans.
Some clans are loyal but the majonty require a loyalty roll when activated.
The result is that they either join one side or the other. Then again they can remain neutral which, in effect, deactivates them. In an historic sense they are waiting to see how the battle goes before commiting themselves to either side. What you can end up doing is spending CPs to activate clans that then switch to your opponents side. The lesson is study the clan table closely.