I'm assuming that you're not talking about the trivial kind of "correctness" where one country/region defines some standard of character usage, and anything outside of that standard is "incorrect".
Why is 纔 the “correct” traditional form of 才?
There is no "correct" form of a character representing a meaning like only; just; merely, because there is no character which was created for this purpose. This is unlike some other character pairs, where you can be sure that one variant is more "correct" than the other, or at least has a much better historical precedence (e.g.「气」is definitely "more correct" than「氣」; the former depicts the word it originally represented, while the latter is a phonetic loan).
Bear in mind what the book you're reading is actually about; apart from the possibility that the choice of「纔」over「才」is just as a result of personal preference, there are real disambiguation reasons for which one might choose「纔」over「才」:
- 「纔」originally described a blackish colour of an item of clothing, and now means some kind of blackish colour in general;
- 「才」was originally a picture of a wooden object, and was extensively used for
- material/resource (材)
- wealth (財)
- talent/genius (天才)
- phonetic loan for「在」(pre-Qin)
If one is talking about language, especially archaic texts, the chance of reading ambiguities popping up is much higher with「才」than「纔」.