This is a few days old, but if you're still interested, here is the short answer.

The 'State Sponsor of Terror' list is only a few decades old, having been founded on Dec. 29, 1979. Cuba was added in 1982, under the Reagan administration.

Cuba's fight against apartheid South Africa was not, to my knowledge, ever through direct aid in South Africa itself, though this is possible. The main point of conflict with the South Africans was the conflict over Angola. Since the late 70's the Angolan government asked for Cuban help to stay independent, after the Portuguese left, and South Africa supported warlords who could be made into puppet rulers of the country. Keep in mind, the South Africans were already in Namibia, which they controlled militarily. That really pissed Washington off and was an important reason that normalization in the 70's, especially under President Carter, didn't go farther than it did.

But what really pissed of the Reagan administration in the 80's was Cuba's aid to Central American countries, like Nicaragua and El Salvador. Remember, we're in the build up to US support of the Contras, the US is also supporting hard line governments in the area. Cuba is providing training, arms and technical support to leftist governments in the region. This angered the Reagan administration to no end.

The US couldn't respond to Cuba 'meddling' in American affairs by attacking Cuba directly since that would escalate into conflict with the USSR. The solution was therefore to use the mechanisms they had, like special economic sanctions, to pressure Cuba to leave the region alone.

Couple of books worth reading:

-That Infernal Little Cuba Republic by Lars Schoultz.

-Back Channel to Cuba, The Hidden History of Negotiations Between Washington and Havana by Peter Kornbluh and William LeoGrande