≒ Aren't you the one who will buy it?
≒ Aren't you the one who bought it?
The difference between 買う and 買った should be straightforward; whether you will buy it in the future or you bought it in the past.
The use of た at the end of the sentence should be the tricky part, and it does not describe something in the past, at least directly. Basically, using the ta-form in a sentence like this would make the sentence sound more euphemistic, mild, less-confident, or "polite".
By the way, a typical reaction to these questions would be 「あ、そうだった」 (≒"Oh, that is right."), also using the "past tense". Here's why.
English speakers also often use the "past tense" when they want to say something politely and indirectly. Compare "I wonder if you can ..." and "I was wondering if you could ...".