They were born in Spain and held high positions of power in the colonies.
Their dominance lasted throughout the colonial period, which spanned from the 16th to the 19th centuries.
So, instead of asking "when was peninsulares?", you might ask:
* When did Peninsulares rule in Spanish America? (Answer: 16th - 19th centuries)
* What were the causes of the decline of Peninsular power in Spanish America? (Answer: Factors include the rise of Creole nationalism, the weakening of Spain's power, and the influence of Enlightenment ideals)
Let me know if you have more questions about this!