In the 17th-century there were already some who were trying to separate out the "scientific" parts of alchemy from the "magical" parts, turning those parts into what would be eventually called "chemistry." It wasn't an overnight thing; it certainly had occurred by the Chemical Revolution of the 18th century, but it's also clear that even pioneer "chemists" like Robert Boyle still thought of themselves are alchemists on some level (just "better" alchemists) and still drew upon classic alchemical notions in their work.

It's in the 18th century though that you see a strong rhetorical separation of alchemy from the work the self-described chemists were doing — they identified what they were doing by what they were not, which was defined as all of the magical aspects of alchemy, which led them to, for example, pick out all of the "good" stuff of Boyle and count him as a chemist, ignoring all of his alchemical work. In reality the lines between alchemy and chemistry were pretty blurred throughout its history; it was the chemistry of its time, and was not only obsessed with magical/religious notions, though those were part of a lot of the work that was done, even the "naturalistic" work.

So the answer, in brief, might be something like: the actual practices shifted gradually over the course of the 17th century into the 18th century, but the rhetorical separation happened a bit later, as part of the professionalization of chemistry. As with all broad historical trends, drawing the exact line is difficult (there were some medieval natural philosophers who derided alchemy, for example, and the account above is entirely European-based, arguably mostly concerned with work in England and France; the history of alchemy is much more than that!).

Further reading: Lawrence Principe, The secrets of alchemy, and William Newman, Atoms and alchemy, are both very reliable, standard references about the early modern history of alchemy.