He was an oidor (judge) in the Audiencia of Santa Fe de Bogotá (also part of the Viceroyalty of Peru), beginning in August 1674.
Mata Ponce de León was named president of the Audiencia of Quito by a decree dated October 27, 1689, but he did not occupy the position until January 10, 1691.
In 1693 he sent the oidor Cristóbal de Cevallos y Borja to supervise the design and construction of Guayaquil.
Mata took care that the sick were aided and medicines distributed, applying some of his own money to the purpose.
Finally, on June 20, 1698, another earthquake destroyed what little of Latacunga had been reconstructed, and also badly affected Ambato and Riobamba.
Thereafter the king offered to promote him to a place in the Council of the Indies as a reward for his services, but Mata preferred to remain in the administration in Lima.
Mata, in virtue of his position as deacon of the Audiencia of Lima, was named interim governor and captain general of the Viceroyalty of Peru.