Quintón was born in Caguas, Puerto Rico into a musically talented family. His father, a Frenchman by the name of Juan Bautista Quintón y Luzón, was a graduate of the Conservatory of Music of Paris. The elder Quintón was also a composer and organist who became his son's first music teacher. When Quintón was two years old his family moved to the town of Coamo. In Coamo, he took piano lessons with Ernesto del Castillo. In 1890, when he was nine years old, he performed his first concert. When he was only eleven years old he accompanied the famed Cuban violinist Claudio Brindis de Salas Garrido on the piano in a concert and was highly acclaimed by him. Quintón continued to study music and was the director of his school's band. During his spare time he gave piano and violin lessons.