Cuban seed describes the plant’s ancestry, not where it was grown. After the embargo, growers took Cuban seed to Nicaragua, Honduras, the Dominican Republic, and other countries. Habano, corojo, criollo, and related varieties belong to this group. The plants grow in different soil and climates. The cigar is Nicaraguan, Honduran, or Dominican unless the tobacco was grown, and the cigar was made, in Cuba.
Padrón describes its tobacco as Cuban-seed, sun-grown, and Nicaraguan. That describes both the seed and the country of origin, and both can be true at the same time.
Do not take “Cuban-seed” to mean the same thing as cuban cigar. After 1959, the Cuban tobacco industry and the Cuban seed went separate ways.