If your table is truely extended, then that logic exists on your extended table.   However, there may be conditions that prevent it from running, and those conditions could be in many places.

Class = Incident would not run for your extended table

Class IS A Incident would run.   I doubt any OOB logic would use this as a condition.

In the OOB incident events, I don't see anything that would prevent it from running on an extended table.   So, I question whether what you did was actually extend it.   If you go to the incident table, do you see the records in that table for your extended table?   You mention Parent/Child, did you actually just create a child record of Incident (like Incident Task)