So you are not proposing a continental bridge across Antarctica, travel through North America, or a separate evolution for south american monkeys.
No, he's not. South America and Africa were once joined, with neither of them being in their current location.
What would cause a mega-continent to hold together for so long and then suddenly (relatively speaking) drift thousands of miles apart? Also, such an explosive speciation timewise among all animals in South America including boas?
The causes driving tectonic activity are not entirely understood. That continents are moving is well documented by direct observation, and there is plentiful evidence from numerous sources that South America and Africa were once joined - from the brute matching of their coastlines, to the continuity of geological strata across where they once joined and the correlation of paleomagnetic records to the matching of fauna.
This breakup began some 170Ma ago, and the atlantic opened up around 110Ma ago so there has been plenty of time for dramatic speciation. Which is just what we see in the very different new and old world monkeys. Other breakups such as Australia and South America from Antarctica, India from Africa and Madagascar from India occurred later and leave their own marks in the bio-geographic record.
Are there any species in South America that match species in Africa with the exception of humans and other plants and animals that could have "grown their way" or migrated across the Bering Straits?
We see numerous examples of species ranges spread across the previous continents in both plants and animals, yes. The spread of marsupials is one of the most striking examples.
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