I have just noticed the following situation in a great campaign:
I was controlling 3 client states when a faction declared war on me. One of them joined the war, the other two refused to do so because they did not like me very much. Now these two factions are independent but not in war with me. There even seems to exist a truce between us, so I can not attack them without losing diplomatic reputation although it would be my right to subjugate them again.
I am not sure but I think in previous versions refusing a call to arms meant war with your former overlord as a client state or satrapy.
Total War Rome 2 Client States
Rome 2 Client States At War With Each Other
Client states are forced to give you yearly income, albeit small, that is always welcomed. In some cases certain provences & regions are heavily steeped in a cetain culture / religion; rather than trying to send a dignitary or build buildings & deal with unrest, having a client state of that culture / religion manage that all the while being. Cilicia (CCI): As one of the richer Anatolian regions, often used as a staging ground for the armies of the successor states, Cilicia can also support its own regional kingdom. Crete (1KR): Should one Cretan state come to control all the important cities of the island it can assume a new pan-cretan identity.