I doubt that it matters a whole lot whether human evolution began in Mesoamerica or in Africa pertaining to animal domestication. Diamond writes in pages 168-175 the reasons for there being only 14 ancient species that were domesticated were: Diet, growth rate, mating habits, disposition, reactions to danger, and social hierarchy.
In class we discussed that had humans evolved in Mesoamerica as opposed to Africa, then the animals of African descent wouldn't have evolved alongside humans and therefore wouldn't see them as a danger. Thus, it would have been much easier to domesticate some of the animals from Africa. However, I don't think that the presence or absence of humans would have a drastic affect on the African animal's reaction to danger or their nasty disposition. There were 51 species in Africa that could have potentially been domesticated, but many had an instinct to panic and try to get away (such as gazelles) or to always be aggressive and unpredictable (such as buffaloes) . Yes, this could have been in part the fault of human's hunting, but there were 50 other species whose hunting contributed to these species's nasty dispositions or instinct to panic. So if humans had slowly moved from Mesoamerica to Africa, the animals there would still be impossible to domesticate.
It also wouldn't have mattered whether humans evolved in Mesoamerica or Africa first because they would have still domesticated plants around the same time as the real course of history. In Mesoamerica it wouldn't make sense to domesticate plants because they didn't have very many to choose from and those they did have would either take too long or not produce enough for everyone. Since they couldn't take that first step and domesticate plants, they wouldn't have anything to sustain an animal's diet. It wouldn't be until they got to Eurasia and found plants that could be easily domesticated, that humans could begin to domesticate animals.
I think there wouldn't be much change in how societies would develop over the course of history if they had evolved in Mesoamerica or in Africa, because in either situations they would have to wait until they reached Eurasia to begin to domesticate animals