ومن أسلم أو ولد بعد طلوع الفجر لم تجب فطرته
Translation: One who accepts Islam or is born after dawn does not incur fitrah for that Eid.
In the first scenario, someone accepts Islam after dawn on Eid. At the determining instant the relevant condition was not present, so fitrah is not imposed for that Eid.
This is a time-specific ruling, not a claim that a convert can never be liable for fitrah in later years.