This really doesn't have much to do with the US, as much as it has to do with the different Spanish colonial histories of the the two countries.

Puerto Rico (and the rest of the Caribbean) was essentially de-populated over the decades of the early 16th Century, though enslavement and successive waves of epidemics. The islands were then re-populated with arriving Spanish (and later, other European groups, as well as enslaved Africans). The Spanish priest (and early Caribbean colonist himself) Bartolomé De Las Casas wrote a famous polemic, A Brief Account of the Destruction of the Indies, wherein he paints a vivid picture of what was happening on the islands during the early Spanish period. This is his famous passage about Hispaniola:

And this was the great care they had of them, they sent the Males to the Mines to dig and bring away the Gold, which is an intollerable labor; but the Women they made use of to Manure and Till the ground, which is a toil most irksome even to Men of the strongest and most robust constitutions, allowing them no other food but Herbage, and such kind of unsubstantial nutriment, so that the Nursing Womens Milk was exsiccated and so dryed up, that the young Infants lately brought forth, all perished, and females being separated from and debarred cohabitation with Men, there was no Prolification or raising up issue among them. The Men died in Mines, hunger starved and oppressed with labor, and the Women perished in the Fields, harrassed and broken with the like Evils and Calamities: Thus an infinite number of Inhabitants that formerly peopled this Island were exterminated and dwindled away to nothing by such Consumptions.

He then goes on to state:

In the Year 1509, the Spaniards sailed to the Islands of St. John [Puerto Rico] and Jamaica (resembling Gardensa and Bee-hives) with the same purpose and design they proposed to themselves in the Isle of Hispaniola, perpetrating innumerable Robberies and Villanies as before; whereunto they added unheard of Cruelties by Murdering, Burning, Roasting, and Exposing Men to be torn to pieces by Dogs; and Finally by afflicting and harassing them with un-exampled Oppressions and torments in the Mines, they spoiled and unpeopled this Contrey of these Innocents. These two Isles containing six hundred thousand at least, though at this day there are scarce two hundred men to be found in either of them, the remainder perishing without the knowledge of Christian Faith or Sacrament.

The Spanish, to put it simply, were first able to brutally exploit the indigenous populations of the Caribbean. Then, perhaps as early as 1507, smallpox arrived on Hispaniola and proceeded to spread throughout the region. Subsequent epidemics, both of smallpox and other infectious diseases would follow. We don't have very good numbers on the population decline in the Caribbean, but in Mexico we have better estimates of how waves of epidemics hitting a disease-naive population already under a significant labor burden reduced the population from ~20 million to ~1-2 million in the course of a few decades. In Mexico, the population crash, subsequent fracturing of society, and on-going oppression from increasing numbers of European colonists, was enough to make the indigenous populations minorities in their own country. In the Caribbean, it was enough to basically eradicate entire groups of people.

The Philippines also suffered from the introduction of new diseases. The distance between Spain and the Philippines, however, could act as a buffer, as did the fact the route between those two regions actually passed through Mexico. Acapulco was in fact built to facilitate trans-Pacific trade, with Manila as the destination port. The distance, the climate, and the fact that Mexico acted as the middle port on the trip also helped to somewhat inure the Philippines to Spanish colonization, which was never as numerous nor as effectively implemented as it was in the Americas. De Bevoise, in Agents of the Apocalypse: Epidemic Disease in the Colonial Philippines, actually makes the case that it wasn't until the later Colonial period -- really not until the 19th Century -- that the opening the Philippines to countries other than Spain, combined with increasing unification of the archipelago, really brought the ravages of sustained epidemics. The Philippines, in other words, did not experience the sort of massive, early demographic crash as occurred in the Americas, nor was Spanish colonization as robust, which created the conditions for sustained Spanish-speaking populations in the Americas.