Well the symbol they use with the Out Of Africa logo is a tiger face, so there is not much geographic consistency here. (They also have indian nilgai and asian water buffalo on the african savannah).
looking through the gallery I think that's a bit of a harsh statement. I don't like the misleading name of the place, but the enclosures for most of the animals seem quite reasonable, or even very good for the hoofstock (not that I can judge the size of them). This marmoset cage seems pretty large relative to what a lot of zoos give them, even if it has a dubious title and lack of greenery.
Did Arizona Docent say somewhere in one of his posts that this is a "rescue" centre? Or was that a reference to somewhere else?