Thanks for your question! To clarify, are you referring to notifications for a rule that is sent from Automation? Or are you referring to comments added to tickets that are performed by an automation rule?
If you can send a screenshot of an example of this comment you are seeing, that will help us in figuring this out for you. Looking forward to hearing back.
Jane (Jira Automation)
Thanks for your reply and the screenshot.
It looks like a rule has been set up to add a comment onto an issue when a linked issue has been resolved. If this is not what you want your rule to do, you (or your global admin) simply need to find that rule and disable this.