What were the practice and/or policy changes about the routes during this time?
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Even before the Iberian Union, we already know of several notable Spaniards who traveled to Asia on Portuguese vessels on the Carreira da Índia, namely Francis Xavier and two Spanish Jesuit colleagues. Further, it is known that many Portuguese sailors and navigators entered Spanish service prior to the Union, including the most well-known of them all Ferdinand Magellan. Up to the late 1600s, Portuguese seamen continued to be present in Spanish Americas and in Spanish service in general, both at sea and on land. But the opposite is much less true, in particular in the early period prior to the Union in 1580.
To know why, we have to see the nature of the Spanish venture in the her New World Empire and the Portuguese venture in her Empire. The former relied more on private enterprisers while the latter relied more than royal prerogatives. Most Spanish vessels were privately owned while on the Portuguese side it was the opposite. So the degree of royal control over the fleets were very different. The Spanish largely controlled their trade through taxation, regulation, and organization.
This is not to say they were fully tolerant of Portuguese participation, as we also know of various edicts in 1590s -- during the Union -- whereby a Portuguese merchant from Macao found his way to Acapulco only to be arrested and sent back to Portugal. So the issue is, Portuguese were allowed to operate in the Spanish system, but only if they were serving the interest of Spain. For example, that Philip II and III granted the Portuguese the privilege of supplying slaves from Africa to Spanish Americas. In this period, Portuguese merchants also provided provisions to Spanish colonies in the Americas, even if there were no clear regulations whether they were allowed there nor if they had any rights, outside specific edicts. Regardless, there was a draw to Portuguese emigrating to Spanish America, for they numbered around 6,000 in Peru in 1600.
The converse, the Portuguese employing Spaniards, we can surmise is true, especially given that the Iberian Union completed the transformation of the Portuguese Imperial administration to copy the private-run enterprise of the Spanish Casa de Contratacion model. But this is an area that is under-studied and I do not have any examples to give; it also comes at a time when the Portuguese were in decline in Asia. Simply put, there was less favorable risk/reward for Spanish nobles to serve in the Portuguese empire than there was for Portuguese nobles to serve in Spanish Americas and beyond. When we speak of sailors, seamen and traders, records available are really lacking that it's hard to make a quantitative statement.
Want to know more? Subrahmanyam's The Portuguese Empire In Asia: 1500-1700 is a delightful read, as is Hawke's The Portuguese in Spanish America.