When the newly refurbished Sag Harbor Cinema opens its doors, presumably sometime this spring, and patrons are finally able to settle into the comfortable, brand new seats for a state-of-the-art film experience in one of its three theaters, they just might encounter a familiar face running the place — especially if they have been regular customers of the nearby UPS Store. That’s because Thierry Balihuta, 33, who joined the staff last fall as the cinema’s manager, most recently managed the Sag Harbor UPS Store where he could be relied upon to help customers ship parcels, design brochures or produce marketing materials.