I think this still leaves open the question: why didn't the autocrats run the tiger economies to the ground? This model is also incredibly similar to The Dictator's Handbook.
One of the reasons why Singaporean and South Korea did not go the way of Russia, Bourbon France, and Habsburg Spain, is that those economies just didn't have enough resources. They didn't have the "resource curse". Therefore, the only way out was up: they had to build the economy. But I don't think this is a sufficiently compelling explanation, because these autocrats could still have extracted far more than they did.
Take Park Chung-hee in South Korea. While he did enrich his family, it was nowhere near the level of Obiang in Equatorial Guinea or Marcos in the Philippines. The Singapore leadership under Lee Kuan Yew paid themselves high official salaries but didn't engage in massive personal appropriation of state resources. This restraint wasn't obviously necessary for regime survival.
I think a large part of the explanation is that the tiger economies simply lucked out with their founding fathers, much as India lucked out with an excellent first cabinet (Nehru for prime minister, Patel for state-builder, Ambedkar for the constitution writer). Lee Kuan Yew's speeches and writings show a man genuinely obsessed with the intellectual and practical challenge of transforming a resource-poor island into a first-world country. I know less about Park, but he seemed to have admired the Meiji transformation and have seen national development as a personal calling.
The book calls German and Soviet expansionism consumption spending by their respective autocrats, Hilter and Stalin. The tiger economies' sound economic policy was consumption in the same way for their leaders. The tiger economies were passion projects.
I think this is not such an absurd claim to make: there are strong selection effects at work here. The autocrats of the tiger economies were a self-selected lot. What fool, but a highly competent and patriotic one, would take on the task of steering a breakaway Malaysian island? Compare this to a resource-rich country like Russia, where riches are guaranteed if you can claw your way to the top.
Another example of a highly competent statesman is Seretse Khama, the first president of Botsawana. He was especially unusual in that he overcame the resource curse of Botswana's diamonds. According to his Wikipedia, he enforced strong measures against corruption, promised mining companies low taxes and encouraged them to explore more mines, resisted calls to "indigenize" the bureaucracy and kept the foreign expatriates who staffed it, drew on international advisors and consultants, invested in education and healthcare, spent shockingly little on defense, and even negotiated the end of the Rhodesian civil war and the independence of Zimbabwe as a little side project before his death. Between 1960 and 1980, Botswana had the fastest-growing economy in the world.
How do you explain Khama? A stationary bandit whose optimal exploitation rate happened to spur outstanding outcomes? Or a bandit who drew the Laffer curve wrong? Maybe the Occam's razor explanation is the correct one: Botswana lucked out.