The personal savings allowance (PSA) means you can earn up to £1,000 from savings interest without paying tax. However these reward payments don't count as savings income for tax purposes and instead are classed as 'annual' or 'miscellaneous' payments. This means the rewards don't count towards your PSA, and they're still liable to be taxed.
If you're a non-taxpayer, you should claim back any tax taken using the R40 form. Higher and additional-rate taxpayers may need to pay more via tax returns.