How did the zombies survive the nuke in "Resident Evil: Apocalypse"?

The honest answer can be found at BoxOfficeMojo:

"Resident Evil" is one of the oddest film series because it's actually gotten bigger box office over time. PT Anderson may have been thinking the second film would be it, and so destroyed the zombies, only to find that $129M wouldn't be ignored.

And the more successful they are, the more freedom he gets and, hey, getting paid millions or tens of millions, even, for hanging out with your wife might not be a bad deal, especially if your wife is Milla Jovovich.

Continuity is not a big thing in these movies however. It's not Friday the 13th level of incoherence, but it's not great.

If you need an "in-universe" explanation, the simplest one I can think of is this: The breakout wasn't limited only to Raccoon City. As a result, even though the zombies there were destroyed, Umbrella Corp was busy making them all over the world. This is actually borne out, as a theory, by one of the opening scenes of RE5 (Retribution), where the outbreak appears to have started in Tokyo. (So, not Raccoon City.)

Later, Alice visits the scene in some kind of holodeck, which you can see on YouTube.