I don't know how their performance influences JIBAR.
It doesn't. JIBAR is the Johannesburg Inter-Bank Agreed Rate and is quoted every morning as the average rate that banks will lend to each other for a certain term.
JIBAR is not one rate, there are many different JIBAR rates e.g. 1-month JIBAR, 3-month JIBAR, 6-month JIBAR etc. The most commonly used one is 3-month JIBAR (this is the rate most people are referring to if they just say JIBAR) and I think that is the one that SA Home Loans uses