For starters, about a century separated Newton and Kant -- so Kant could hardly have been reacting. Secondly, there was no "inductive Aristotelian paradigm that held sway at the time" -- this kind of debate was further back a few centuries. Kant was in any case well-versed in Newtonian physics and the mathematics of the time, and his philosophy wasn't meant to be a reaction to it. Newton's mechanics worked in the sense of explaining and predicting a number of superficially disparate phenomena and Kant would have been well aware of this. Secondly, Raynes seems to be ascribing a solipsistic position to Kant, which can't be right. It's true that Kant considered space and time categories created by the human mind, which made possible some sort of human-based understanding of the world around us -- but that is not solipsism; it is different and it is deeper. This understanding can be empirically corroborated. Yet while Kant is not advocating rationalism, he is also not advocating empiricism; it is something beyond. We understand the world in a certain way, and that understanding can be empirically tested, but we only know surface phenomena: we can't go beyond that to some mysterious "thing-in-itself."
If memory serves, the true accomplishment of Kant was not to react against Newton and mathematical physics but to demonstrate that metaphysics was impossible -- that the human mind could only grapple with some (anthropomorphically conceived) aspects of phenomena in this world and the rest is idle and fruitless speculation. Along the way, he came up with some interesting ideas -- for instance, the "synthetic a priori." That there exist analytical a priori and synthetic a posteriori is more or less tautological, but not so the synthetic a priori. Kant's Critique of Pure Reason is the first book I know where reason is carefully exploring itself, its possibilities and limitations. I agree with Bryan Magee who, in his Confessions of a Philosopher, calls Plato, Aristotle, and Kant the three giants of Western philosophy.
I'll have to hit the books if I have to write more at length and even to correct some of the above and sharpen the language. It's been written extempore.