How does property tx exemption work for 100% SC vets?

I am a 100% disabled vet and plan to buy in a state in which I can be awarded a full property tax exemption. Outside of knowing there is a cut off date to apply for the exemption very early in the year, I don't know anything else about the tax exemption – i.e. when it actually takes effect. Is it an annual reimbursement or can it take a effect during the home buying process so tax is not rolled up into your estimates? Just curious to know if I would have to wear the burden of property tax at anytime?