This discussion from a few days ago is relevant to your question. There are several layers in your question and the answer(s) depends on which layer and period one addresses.

First of all, it is important to understand the distinction that separates mythology and belief system - the everyday religion of most people. Because the classically-written mythology of Greece or any other ancient culture represents that best available body of documentation about belief systems of the period and places, it is easy to think of that body of literature as being the same as a belief system - but it is not. The documents that describe mythology are artificial constructs of a literate class that was attempting to record but also to reconcile differences in the stories and the belief systems of a people. At best the mythology was a step removed from the belief system, but in reality it was likely very far removed from what constituted the religion of the everyday people. But because we have no other documents that record the religions of everyday people, we can only speculate on what was practiced and believed based on the process of connecting scattered dots from diverse bodies of literature and from archaeology.

That said, literature typically has the ability to back feed into popular belief, affecting religion and stories by offering the "definitive" version, so the written myths of a people probably had an increasing effect on what was believed. The literate class of the ancient world was keenly aware of this important part of its cultural and religion patrimony. The mythological texts were "taught" in a sense to those who could read. The average person would have access to the stories related to his/her culture and religion through the oral tradition of the period and place, and this oral tradition was probably increasingly affected by the recorded mythology.

People have consistently sat "around discussing" all sorts of aspects of the supernatural, so we can assume that the everyday people of the ancient world did the same. Folklorists recording pre-industrial Europeans discussing supernatural beings of nature documented animated debates about what the stories meant, about how contradictions could be reconciled, about how powerful these entities were, and about how to approach them with appropriate caution and deference. These pre-industrial people believed they lived concurrently with the supernatural beings, although there is some evidence that the folk also consistently asserted that previous generations had more active belief and were in more consistent contact with the supernatural - back in the elusive "good old days." These sorts of encounters have consistently produced new stories about "what the supernatural beings have been doing" as you say.

By analogy, what was scientifically, professionally recorded from pre-industrial Europeans can be taken with some caution to help us understand what the average illiterate Greek in a remote village thought of the supernatural. We can't know for sure because of the lack of documentation, but the analogy provides some insight.