If a user can create an item for someone else, you would need to identify how you are storing that separation in the actual incident and carry it over to My Items. Then add another object permissions rule to account for the new field.
The OOTB rule pulls on CustomerRecID, which is just the RecID from ProfileLink.
If you are utilizing the OOTB link field for 'Reported By' you can copy the same thing profile link is doing but with alternatecontactlink_recid to some new field in FRS_MyItem, like ReportedRecId. Then build your object permissions rule from that.
The goal is to make it to Self Service can see my Items where CustomerRecId OR ReportedRecId is equal to them. They would then be able to see items logged for them and logged by them.