But if Eurasia is more advanced medically, there is the possibility to distribute vaccines to the Americas.
Depends how early they get them. If they don't get it until 1600 or so, the damage has already started.
Plus there's the issues that happened historically, like how once in the early 19th century, the US government spent money trying to vaccinate Indians. The money earmarked for it ran out sometime after they finished vaccinating the Sioux, so next smallpox epidemic ended up destroying most of the Sioux's enemies while sparing the Sioux, the end result being the Sioux were able to utterly wreck their longtime foes.
Substitute "Sioux" for your native group of choice to see what might happen.
Agreed that the later it happens, the less effective it is. Of course, the converse is true: the earlier it happens, the more effective. If the technology is known while there are still viable indigenous states in the New World, and the information on how to vaccinate spreads to them, there's nothing stopping them from doing it themselves, in order to survive the epidemics.
This AHC being kinda crazy, I don't know at what era this would start to happen, but let's say Renaissance. By that time, the two biggest are gone (Aztecs, Inca), and everything else is a variety of loosely organised chiefdoms at best, or states being heavily, heavily pushed by the Spanish. The best bet is probably things like Jesuit missions spreading these, meaning people like the Bandeirantes would have a very difficult time. And the Spanish themselves, since they might not like the fact all their Native American slaves/serfs die so easily so why not investigate this "germ theory" and "vaccination"? Which means the trans-Atlantic slave trade will be much lower in size, and means the indigenous population of the New World will be larger and even more of a component of the population makeup to the point where your average Latin American is basically a Spanish/Portuguese speaking Indian.
Lots and lots of butterflies everywhere, of course.