He made his formal entrance into Mexico City on August 16, 1716, and received his office from the previous viceroy, Fernando de Alencastre, 1st Duke of Linares.

Viceroy Zúñiga sent a ship from the Armada de Barlovento (coast guard) to pick them up and transport them to Veracruz.

In 1722 Juan Ignacio María de Castorena Ursúa y Goyeneche began publishing a newspaper in Mexico City.

On June 16, 1718, as the viceroy was leaving the procession of Corpus Christi with the Audiencia, he was attacked with a knife on the stairs of the palace by a man named Nicolás Camacho.

During his tenure as viceroy, Zúñiga was faced the issue of the British colonial settlement at Laguna de Términos (in present-day Campeche).

This site had been occupied almost continuously since 1663 by English-speaking buccaneers and colonists who harvested tropical timbers in violation of Spanish law.

In 1716, Zúñiga sent a Spanish fleet from Veracruz, under the command of Alonso Felipe de Andrade, to liquidate the British settlement.

The valuable property captured by the Spanish from the settlement, including harvested timbers, amply repaid the costs of the expedition.

The viceroy sent the Marquis of San Miguel de Aguayo and 500 militiamen to expel the French from the Bay of Espíritu Santo, where they were established.

For the marriage of the Prince of Asturias to the Princess of Orléans, Viceroy Zúñiga was named majordomo of the palace in Madrid.