[clause],[subject] + 反而 + [verb phrase]
[subject] + 不但不 / 不但没 + [verb phrase],反而 + [verb phrase]
反而 introduces a result that is the reverse of what the first clause should have led to. It goes in the second clause, after the subject and before the verb.
The fullest form spells out the expectation that failed, then the opposite that happened.
反而 needs a cause that pointed the other way. Choosing tea over coffee is a plain contrast, not a reversal, so it doesn't take 反而.
反而 is an adverb, so it can't go in front of the subject.
却 also marks a turn in the second clause, but only "yet"; 反而 says the outcome reversed.