Integration type response-1

How often is Automation response updated on the target (ITSM) system?

I am not sure about your question.
ITSM has its own logic and if it is about automation, it depends how the process has been implemented and the frequency of its execution.
The processes will not execute automatically based on certain events, besides manual execution or through API.

When you create an Integration Type Configuration, there is a checkbox option to Update Response via Integration Service. The Integration Service has a scheduled job that runs every 30 seconds (configured while Integration Service Registration) to update the execution response on the ITSM system.