Given their respective roles as warrior and subordinate, Tygett and Kevan were almost certainly there. Gerion probably not.
Tygett however could have been good option to leave to Casterly Rock in case another army must be raised right? But I suppose Tywin could have thought that there would be no need since Rebels had practically won already.
Also, Tygett’s temperment is much better suited to being in the field and on the attack as opposed to an organizational role on the homefront.