All the time actually, at least when the spread of disease didn't completely outpace the spread of Europeans. The 1637 outbreak of influenza in Wendake provides a great example of the evolution of thought on the subject since we have a fairly detailed account of the incident.

Wendake is the region between Lake Ontario and Georgian Bay in Ontario. At the time the people of this area - the Wendat, also known as the Huron - had most of their villages in the western portion of this area.

Initially the disease was thought within the normal context of Wendat disease theory - ie, some oki was royally pissed off for some reason and needed to either be appeased with feasts and dancing, or at least convinced to rampage among the Wendat's enemies rather than sticking around here. And, of course, the incorporation of a spiritual aspect to dealing with the disease didn't preclude quarantining and tending to those who were already sick. Later the idea that an indigenous oki was responsible fell out of favor and instead a popular theory, originally devised by the Algonquin to the east, was that the disease had been unleashed by the vengeful sister of Etienne Brule (a trader who had died under mysterious circumstances while in Wendake). Brule's sister wasn't the only suspect; the missionaries themselves were occasionally blamed, particularly since they always seemed to flock to the dying in hopes of scoring a few deathbed conversions.

Two years later, an epidemic of smallpox confirmed that these new diseases were emerging from the French. Here's father Lalemant on the topic: "They observed, with some basis in reason, that since our arrival in these lands, those who were nearest to us happened to be those most ruined by the diseases and that the towns that welcomed us now appeared utterly exterminated. [...] Wherein truly it must be acknowledged that these poor people are in some sense excusable. For it has happened very often and has been remarked more than a hundred times, that where we were most welcome and baptized the greatest number of people was in fact where the greatest number died. Conversely, in the cabins to which we were denied entrance, though they were sometimes extremely sick, at the end of a few days one saw every person happily cured." Once it became clear that these diseases were connected with the French, the missionaries were banished to the southeastern outskirts of Wendake.

I have a more detailed version of this incident here if you're interested.

Two other notable examples come to mind as well. A major epidemic struck the East Coast in the 1610s, hitting southeastern New England particularly hard just prior to the establishment of the Plymouth Colony. Europeans had been in New England, off and on, for nearly a century prior to that and the new diseases were associated with them by the time the Mayflower arrived. According to Governor Bradford, Squanto himself exploited this knowledge, claiming that he knew where the English hid their dreaded biological weapons and threatened to release those pestilences himself should the need arise.

Even before that, in 1598, the Roanoke colonists (specifically Thomas Harriot and his small party sent to explore the mainland of the Carolinas) encountered people who quickly realized the connection between newly arrived people and newly arrived diseases. Harriot's party seems to have been spreading some sickness among many, but not all, of the villages they visited. The people from infected villages sought Harriot out, begging him to remove whatever curse he put upon them, but he thought the sicknesses were divine judgment dealt out against only those villages who had wronged him through some trickery while he was on his journey.