There is an option to enable Aha! notifications for comments on records made via an integration. Even when this is enabled, if you are the callback user for an integration, you will not receive notifications about comments synced in via that integration.
In most cases, skipping notifications for changes made by your user makes sense. In this scenario, even though you are the callback user, you are likely not the user adding comments in the external tool, and so might still want to proactively receive them.
Either send notifications for all integration comments when you have that option enabled, even if you are the callback user, or add a new notification setting to enable this behavior.