Chai tea is an Indian drink with a specific spice blend, and, in India, a specific process involving condensed milk. Its actual name is ‘chai masala’, which is Hindi for ‘spiced tea’. When white westerners found it, we straddled the line between ‘exotic’ and ‘palatable to anglophone audiences’, and in doing so, made a phrase redundant in two languages. It would have been fine if we’d called it ‘masala tea’ or ‘tea masala’, or just ‘spiced tea’.
Portugal has nothing to do with it.