Everything I have read on the subject seems to suggest that the trans continental traffic was in abeyance for a thousand years or thereabouts, plenty of time for new diseases to become ingrained in a population, or for new forms of old diseases that might have devastating effects on a population suddenly exposed, maybe measles and smallpox.
that's trans oceanic.
We do know that herpetic viruses were common in Europe at the time of the Greeks, so those viruses very likely made it to South America via the Phonecians. It is unlikely that the South Americans were totally unfamiliar with this viral family.
If there had been an incidence of, for example, a newly mutated smallpox in the Western world in the thousand years between the fall of the Carthaginian empire and the first contact by Columbus, then it would likely have been a nasty plague followed by a recovery in population of those who had or been selected for their genetic capability to develop resistance. Else it would be difficult to explain the difference between the 25% losses in Medieval Europe vs the much higher dieoff posited in South America after Columbus because any prior contact would have brought the same plague had the virus existed earlier. The problem with that theory is that I don't know of any record anywhere in the literature after the fall of the Roman Empire and prior to 1491 of such a plague in Europe.
The only other explanation is that there is some genetic difference between Europeans and South American Asiatic Amerindians (if that's who they were) that made the latter more susceptible to the disease. But there are complications to that theory too!
I happen to know some Chilean Indians who hail from the Southern end of the continent (they're Messianic Jews). Interestingly, they're ethnically white folks! They bear no resemblance to either the Amerindians or the negroid Olmecs in either skull shape, cheeks, eyes, etc. She says she has a lot of relatives like her, some with red hair (her kids both do).
So, there are several possibilities. We may never know, which certainly makes for an interesting world.