His name first appeared in a document dated May 25, 1694, when the cathedral chapter provided financial assistance following his father's premature death.
On June 20, 1714, Zumaya was promoted to principal organist at the cathedral and was named maestro de capilla when Salazar retired in 1715.
In the villancico Celebren, seemingly unassuming motifs emerge in the accompaniment, gradually intertwining in complex ways to generate a sense of continuous advancement.
Zumaya authored the charmingly jolly Sol-fa de Pedro (Peter's Solfeggio) in 1715 during the examinations to select the Chapel Master at Mexico City's cathedral.
Zumaya's other famous piece, Celebren Publiquen, shows his ability to handle the polychoral sound of the high Baroque era.
The rich textures and instrumental writing reflect Zumaya's "modern" style and are at the opposite end of the spectrum from his anachronistic Renaissance settings.
Zumaya's recessional Angelicas Milicias presents his ability to superbly combine the Baroque orchestra and choir to create a sublime and stately piece in honor of the Virgin Mary.