I work at Nike and I know we use some slightly different names to describe things within Aha to fit our culture, so hopefully you can follow this:
If a user has the Program Epic field set on the FEATURE and on the TEAM EPIC, the Aha system does not seem to be configured to change the Program Epic field on the Team Epic when the parent Feature is changed.
I think it would be good to either have the Program Epic on a Team Epic always set to the value of the Program Epic on the parent Feature. Or make it an optional setting to have those fields linked.
This is important so the fields stay in sync.