In terms of the tax treaty with South Africa (which was specified in the original question)
https://www.irs.gov/pub/irs-trty/safrica.pdf
TAX CONVENTION WITH SOUTH AFRICA
GENERAL EFFECTIVE DATE UNDER ARTICLE 28: 1 JANUARY 1998
ARTICLE 18
is a non-government annuity taxed only in South Africa if the person is a resident alien in the USA? it appears to be so - perhaps better to ask the IRS (in writing).
