I'm no scholar of Newton's life, but I am aware that Newton became a professor soon after attaining his master's degree at Cambridge. I believe he kept this role for the rest of his life in addition to the later posts at the Royal Mint (which were supposed to be merely sinecures, but jobs that he nonetheless took rather more seriously on his own initiative). As for the alchemy, I think one can reasonably consider that science, as the modern principles of chemistry were still a couple of centuries off - Newton did at least conduct proper experiments, which is basis of the natural sciences.

All in all, I think that he certainly made his living from his success in science at first, even if he could have later maintained himself simply on his esteem and lofty networks at Cambridge.