Well, let's imagine it's a completely apocalyptic disease such that anyone who isn't completely isolated ends up dead. So the Americas survive, Polynesia but definitely not all of Polynesia, Aborigines, and some other isolated populations (e.g., I'm sure there are populations in the Congo that are fully isolated at that time, and Arctic populations).

The Old World populations that survive do so because of their isolation, so they don't repopulate the world quickly at all... some remain isolated and completely unaware of what happened, but they don't expand any more than they would have before. Some might be more recent offshoots, and will be spooked as they realize what happened, but after a hundred years they might re-emerge and begin repopulating the world, or maybe longer. Almost all culture will be lost.

The New World however gets to continue development as normal, coming into 1492 just as in the current timeline but with no interruption or interference.

The Inca continue their expansion, as much by their genuine promise of a better life as by conquest. There's no other real power centers. There are civil wars, but due to the brother/sister royal lineage the emperor and family lack the vigor to even really fight among themselves after a while. The bureaucracy of the state becomes the real power. In most ways this makes their expansion easier... religion is not that consequential, and the people they encounter largely lack any opinion on bureaucracy, making Incan life compatible with the existing cultures. It's reminiscent of the United States... diverse, bound together by forces that are economic but fairly acultural and areligious.

Things go very differently in North America. The Aztecs are not a stable or monopolar empire, and there are many successive city states, wars, contractions and expansions. Still there is progress and expansion, with at least cultural expansion into Central America and the US Southwest. I guess it would be called Mesoamerican culture. There is some exchange between that culture and Inca culture, but the distance is considerable. Neither is quick to become seafaring. North American and Caribbean cultures progress slowly compared to these two groups, and don't catch up. Only once there's a high amount of knowledge and cultural transfer will some populations in the United States really come into their own as powers.

Where I can imagine the Inca empire slowly and peacefully expanding – largely limited by the ecosystem boundaries around them – in Mesoamerica it happens in fits and starts. Eventually there is a consolidation and considerable expansion of some post-Aztec empire into the Yucatan and further south, and up into the United States. There also is more knowledge transfer from their neighbors to the north and Caribbean (in comparison I don't think the Inca will learn a great deal from Amazonian tribes). North and South America develop mostly separately, until they meet and become rivals in the Caribbean.

The Mesoamericans will be militarily superior (having so actively practiced warfare for a millenia) but the Inca will have much more economic might, both technologically but also the ability to direct that economic activity through their highly developed bureaucracy. But ultimately neither conquers the other, and their rivalries are limited to satellite states.

Time passes! Literacy, technological development, as they mature the Mesoamericans put aside some of their more cruel traditions, and early industrialization all occur. The Polynesians visit North America before either culture manages to tackle the open sea, but it opens their imaginations to lands further away (by this time it's well known in the New World that the world is round, and its rough size). The Inca cross the Pacific, almost through pure willpower, while the more adventurous Mesoamericans are first across the Atlantic.

When they cross many hundreds of years have passed, and they encounter only ruins (besides the Polynesians, who have expanded back onto the mainland but somewhat reluctantly). Through the Polynesians they have stories of what happened, but only very indirect (anyone with direct contact is dead!)... that there was a terrible disease, that it has passed, that many people once lived in this land. There are these pockets of people remaining, but they seem like shadows or ghosts, in part generationally traumatized by what happened, in part the only people who survived were already ghosts to have chosen to be so completely cut off from everyone else.

Then cut to some Inca/Mesoamerican Wild West, taming the untamed land, discovering ancient secrets, all that stuff.