The quote in question is the following:
For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth.
The common reference for this quote seems to be MacHale's Comic Sections: The Book of Mathematical Jokes, Humour, Wit and Wisdom (p.145) (see e.g. https://mathshistory.st-andrews.ac.uk/Biographies/Stone/quotations/ or Eisner, Farkas, Haase & Nagel's Operator Theoretic Aspects Of Ergodic Theory (p.9) available at https://www.math.uni-leipzig.de/~eisner/book-EFHN.pdf).
I would like to know if there is a written reference for this, or else if it can be verified otherwise. MacHale's book doesn't seem to list references.
Thank you for your time.
I should add that before posting the question I did a fast reference chase which led me to Mandelbrot's Fractals and Chaos: The Mandelbrot Set and Beyond (p.280) (this part seems to be from a reproduction of an earlier Intelligencer article of Mandelbrot, titled "Chaos, Bourbaki, and Poincaré"):
Do not forget that for Bourbaki, Poincaré was the devil incarnate, who had left behind a mess of unproven assertions and loose ends. They boasted that they had cleaned up that mess. Of course, Poincaré has long been a source of concern to French mathematicians. In the 1880s, Hermite kept writing to Mittag-Leffler to complain that young Poincaré never completed a proof. For students of chaos and fractals, Poincaré is, of course, God on Earth.
In light of this the question remains: either the quote is being misattributed to Stone (which seems likely to me, given the bombastic language (I gather from the rest of the book that Mandelbrot really disliked Bourbaki)), or Mandelbrot is quoting Stone. In this book Stone's paper "The Revolution in Mathematics" is listed as a reference; though as far as I can see Stone does not mention Bourbaki nor Poincaré there.