Before I go more into detail on that subject, let me repeat an important point: the SARB does not have an exchange rate target; it has an inflation target.
Furthermore, both theory and experience do show that in the case of the latter, domestic interest rates need not respond to policy rate changes in the US as they would in the event of a dollar peg. If one targets the dollar exchange rate, the interest rate differential with the US is key to sustaining the target.