From Patek Philippe's own guarantee paperwork: "The Guarantee covers all manufacturing faults and material defects as confirmed by an Authorized Patek Philippe Service Center only."
This means that you are responsible for getting the watch to a Patek Philippe Service Center. You got it to a Patek Philippe boutique in Miami. You're halfway there, but not quite all the way.
Hopefully the service center won't charge you for return shipping! I would hope and expect no such charge. But, what I hope and expect is sometimes not always aligned with reality.