Communication Manager does not provide a storage point for external data.
Communication Manager provides a Universal Call Identifier (UCID) value with call events (you have to configure this on in the system - there is a DevConnect FAQ on how to do this provisioning - see below).
The expectation is that an external application such as you are describing puts the call data and the UCID value into a database.
As the call proceeds from the vector handling (or IVR or even some other agent) and is offered to an agent, the call handling application at that device (where again there is a CTI monitor on the device delivering call control events) 'knows' to query the database using the UCID value in CTI event it received for call related data that was previously stored by call handling in an IVR or other point in time (e.g. vector processing).
Related FAQ:
https://www.devconnectprogram.com/site/global/products_resources/avaya_aura_application_enablement_services/support/faq/index.gsp#1000
Related UCID information:
https://www.devconnectprogram.com/fileMedia/download/2f97cad6-c21f-4a56-98ab-1627e604bcb0