You have to remember that the NH rankings are inflated relative to SH rankings due to the fact that they get to play other NH teams. I'm not trying to start an argument, but obviously a team that plays South Africa, New Zealand and Argentina regularly is likely to have fewer wins than a team that plays France, Wales, Ireland, Italy and Scotland regularly.
The system isn't based on the number of wins, but a points transfer system. The greater the difference in rankings, the greater the transfer of points. So, for example, based on current position, if England were to beat the All Blacks they'll get more rankings points than if they were to win a Grand Slam next year.
Whichever side wins tomorrow (England by six) will be ranked third, with a big gap between them and the Springboks and even bigger one to the All Blacks; which I think would be a fair reflection. And the only way for either to climb towards the leaders is by beating them- beating the likes of Italy or Tonga will have no effect.