This is a great question because it pits two central issues of interest to historians: 1) the understanding by past people of their contemporary events/structures/etc. 2) diachronic comparison, thematic analysis, history of processes/institutions/etc.

So, in terms of the Habsburg Spanish Empire, they were not colonies and were never described as colonies by officials or residents. Strictly speaking viceroyalties were not actual entities either. A viceroyalty was merely the geographic expanse of the jurisdiction held by a viceroy. That expanse was never static and was frequently contested. For example, the Audiencia of Panama freqently raised objections to attempts by the viceroy of Peru to exert certain powers over the Audiencia, in particular the power of being the 'capitan general' the Audiencia objected to the viceroy claiming the capitania general of Tierra Firme.

Under the Trastamara/Habsburg model all of the territories of the Americas were considered integral parts of the Kingdom/Crown of Castile, in part because the Kingdom/Crown of Aragon already had overseas possessions in the Mediterranean. The political entities that were established tended to be incorporated as kingdoms (Reino de). So you had the kingdom of New Spain, Kingdom of New Granada, Kingdom of Peru, etc. But those entities were not all equal. As you know viceroys were only sent to Mexico (New Spain) and Peru in the 16th c., and the audiencias of those kingdoms tended to have superiority to the other audiencias subject to the viceroy of that kingdom. But as I said, many lower level audiencias objected to those blanket hierarchies. Santo Domingo always chaffed being subject to Mexico and likewise Panama chaffed against Peru. In part this is due to those audiencias having some primacy in dates Santo Domingo was established before Mexico. Panama had an audiencia before Peru (Panama is weird because the original Audiencia was moved to Guatemala and then a new Audiencia established a few decades later), and lines of communication. Santo Domingo and Panama were both closer to Spain and had faster communication than their superior audiencias. (The jurisdictional history of Spanish America is fascinating and much more complicated than any introductory textbook presents.)

But all of that to say that no, at the time they were not considered colonies in the sense of something added on but outside the prior political order. They were integral parts of the Crown of Castile, and in part the establishment of governance in those regions actually helped fuel regalism back in Spain, as the monarchs began to want as direct control over peninsular Spain as they had in the Americas (and beyond).

But should historians consider Spanish overseas possessions colonies? As a historian who is interested in 'colonialism' I would say, yes. There is a reason to call those entities 'colonies' even if they were not considered colonies by the Spanish. The value of calling them colonies and Spanish expansion 'colonialism' (even though they never use that term either) is that it allows the historian to engage in an analysis that can be directly or indirectly put into conversation with studies of other 'colonies' and 'colonialisms'. While we should always be attentive to the unique particularities of that colonialism (the Spanish considered the Americas an extension of Castile) it doesn't mean that we can't compare it to other colonial frameworks that considered the colonies to be something separate and distinct.