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Based on the article you linked and WHO documents, if you are entering South Africa through Zambia, Yellow Fever vaccination isn't required anymore.
According to WHO 2015, Zambia is not considered a country with risk of infection. You can see the changed requirements from South African immigration here (search for South Africa): 2013 where Zambia was mentioned as requiring vaccination and 2015 where Zambia is now omitted in line with new WHO assessment.
You mentioned "not limited to" transit from Zambia. Make sure your other transit countries are not listed as at risk by the WHO (check out this map for countries with solid red)
or the WHO 2015 list) or ensure your transit is limited to the airport for less to 12 hours (c.f. South Africa section).
who.int/ith/2015-ith-annex1.pdf?ua=1
(Sorry don't have reputation points to include more than 2 links...)
You could double check by contacting the South Africa Dept of Health - switchboard: 012 395 8000