The Spanish sent expeditions all over the Southwest very early after conquering Mexico. They would hear about the Cal Inca very quickly, and it would draw in conquistadors like flies. For all the talk about "the Spanish wouldn't get lucky a third time," remember that they only have to get lucky one more time, and there will be plenty of Spaniards interested in trying. The riches of Mexico (and later the even greater riches of Peru) inspired Spanish conquistadors to go on all sorts of expeditions, waging long and ultimately largely unprofitable campaigns in places like the Yucatan in the hope that they would become the next Cortez or Pizarro. Even if the odds are low (which I dispute; we may only have 2 cases, but the Spanish went 2/2 in those cases), there will be plenty of people rolling the dice.
Once they conquer this region, it will become another major center of Spanish settlement and power, and not one they will relinquish easily. OTL California and what is now the American Southwest were essentially backwaters, scattered with a few missions and small settlements, but with Spain (and later Mexico) only exerting nominal control over most of it. On the other hand; ITTL it will have a large, prosperous native population and plenty of Spanish encomienderos to rule over it. You might even end up with the California gold fields being discovered centuries early, with further resulting development.
In this scenario, the British or Dutch would not be able to intervene without a major expedition, of the sort that isn't practical before the 1700s (and even then, would be difficult and prone to failure, as demonstrated by most of the attempts to conquer Spanish colonies during this time period). Small raids or tiny forts are one thing, but the Spanish wouldn't allow such near a major center of wealth (look at what happened to the French in Florida), and a prolonged military expedition isn't the sort of thing that their rivals would consider at the height of Spanish power.
It will probably become its own viceroyalty (certainly by the 18th century, and probably as early as the 16th), and come independence, become an independent nation in its own right.