To my understanding the CX configurations have to be kept identical manually. From what I understand there is no Failover replication of configurations between the ASA CX in the Failover. Just the ASA configurations
Here is a quote from a Cisco ASA CX Documentations Guidelines and Limitations section
Does not support failover directly; when the ASA fails over, any existing ASA CX flows are transferred to the new ASA, but the traffic is allowed through the ASA without being inspected by the ASA CX.
The above though refers only to the fact that the when Failover happens only the new connections incoming to the now Active ASA CX will be forwarded to it while other existing connections during the Failover will pass the now Active devices ASA CX.
If I am not completely mistaken I think you will need to use the management software on a separate server to be able to keep the configurations synchronized. I dont think the ASAs / ASA-CXs can do that themselves automatically.
Here is another quote:
||To ensure configuration and policy synchronization, make both devices members of the same PRSM device group.
You can either create a new device group and assign the Active/Standby pair to it, or you can simply assign the secondary device to the primary device group. See Assigning Devices to Device Groups for more information.