Do South African expats pay taxes in Dubai?

Dubai does not tax personal income, so your UAE salary is not taxed locally. However, if SARS still treats you as a South African tax resident, you remain taxable in South Africa on your worldwide income – including your salary from Dubai. Simply “moving to Dubai” is not enough to stop SA tax. You can use the foreign employment income exemption (“expat tax exemption”), but it only shields your foreign salary up to a legal cap.
If you want to reduce or stop paying SA tax on your Dubai income, you need to look at changing your tax residency and/or getting a UAE tax residency certificate – this should always be done with a qualified tax advisor.