Ok, I'm going to try to tackle this in a more holistic manner. My apologies for my last answer being not thorough enough. The short answer is this, the One Child Policy's exception for "minorities" did not result in more prosperity for minorities. Although minorities have enjoyed preferential treatment for certain policies like university admissions, they are overwhelming poorer than average "Han" citizens.

To answer this question, we first need to go into what defines a minority, and what defines a Chinese or a "Han." The fact of the matter is, Han identity is entirely constructed and extremely new. What is a "Han" Chinese? Han Chinese is a pan-national cultural identity that describes "Chinese" people who live in China, Taiwan, Hong Kong, Singapore, Vietnam, etc. However, beyond that its definition is very unclear. There is no linguistic element for defining Hanness. For example, in Guangdong and Hong Kong most people speak Cantonese as the native language. This is a language that is not mutually intelligible with Chinese at all. This is true for many regions in China, including Shanghai, Jiangsu, Fujian, Anhui, Hunan, Hubei, etc. This lack of linguistic consistency in defining Hanness even extends to China's most prominent leaders. If you listen to Chiang Kai Shek speak on some recordings, it's nearly impossible to understand what he's saying if you have only studied Chinese. He's speaking Chinese yes, but his native language was actually the Ningbo language. This heavy accent would follow him for the rest of his life. Mao also had a relatively heavy Hunan accent, although I can understand him decently well. I don't know if there are any recordings of him speaking Hunanese. What I am trying to communicate here is that there is truly no defining "ethnic" traits that can describe Han identity.

So what is Han identity? Arguably, Han identity is not an ethnic identity but rather a national identity. This is further supported by the lack of support for Han identity or Hanness in places like Taiwan or Hong Kong. It was constructed during a tumultuous time in Chinese history. During the 19th century, more and more Chinese immigrants traveled abroad to find work because of economic and political instability at home. They moved places like the United States, Southeast Asia, and even Latin America. However, the abuses they suffered at the hands of cruel employers, not to mention the massacres in the United States in California, Wyoming, and Washington, helped create a certain amount of solidarity between mostly Cantonese speaking immigrants in the US and other Chinese back home in the Qing Empire. This became the impetus for the first popular nationalist political expression, the 1905 Anti-American Boycott.

This sounds all very organic, then why argue that Han identity is fabricated? Part of this is the name itself. It is reference to an ancient Chinese empire that was one of the first to unite "China" as we know it. It creates the impression that Chinese identity as we know it, is an ancient thing that has existed for thousands of years. In reality, most Chinese people historical had little or no cultural connections to people in other localities. During the 19th century Chinese merchants came to treaty ports like Shanghai to do business, but they would essentially only be able to form networks with members of the same localities. This resulted in the expansion of traditional merchant organizations, like guilds, into the treaty ports. The biggest guilds in Shanghai were the Canton Guilds, Fujian Guilds, and Ningbo Guild.

So we've established that Chinese national identity was somewhat organically born, but then who fabricated Han ethnic identity and why? Well after 1911 and Xinhai revolution, the new rulers of China needed a nationalist logic and legendary past to give their new regime legitimacy. By tying proto-Chinese national identity to a legendary "Han" ethnic identity, they could argue that the new nationalist/ethnic logic of government in China was legitimate. This was promoted by Sun Yat Sen, Chiang Kai Shek, and even communists like Mao Zedong. Once in power, the nationalists and the communists both promoted educational campaigns to promote the teaching and use of Chinese language on both Mainland China and Taiwan in order to better cultivate a unified ethnic and national identity. Essentially, they wanted to promote the idea that Fujian, Beijing, and Guangdong were all really "Chinese" at their core.

This is where China's minorities come in. Now, defining a minority in China is similarly difficult. The Hui minority for example, doesn't have their own language. They generally speak Chinese or other provincial languages. Their only defining characteristic is their adherence to Islam. However, various Chinese regimes have promoted the idea of difference and the growth of these populations in order to shore up the cultural differences between Han Chinese and minorities. Dru Gladney's "Representing Nationality in China: Refiguring Majority/Minority Identities" is perhaps the best and most succinct paper on this topic and I highly recommend it. This is one reason why minorities were able to have more children under the One Child Policy.

The reason that minorities are generally poorer than "Han" Chinese is a complex one. Part of this is the "bureaucratic capitalist" nature of China's economy, as described by Maurice Meisner in "Mao's China and After." Essentially, China's minorities are unable to enter government. This is not a legal restriction, but rather a result of racial bias. If you look at party leaders and government officials in provinces with large numbers of minorities, you will find few, if any, minorities amongst their ranks. This limits their ability to form networks and curry financial and business favors or facilitate their own businesses.

Another issue is that even outside of government, the business networks, including provincial and locality networks, that have helped make many Han rich are wholly unavailable to minorities. There is actually one exception to the general statement that minorities are poorer than Han. That is the Korean minority. They've been able to grow wealthy through connections in South Korea, something that other minorities cannot take advantage of.

Finally, geography is a key part of this discussion. Generally, China's minorities live in inhospitable places with poorer quality soil and farther than inland and away from the economic development that has marked China's coasts. Many minorities were pushed off their lands or assimilated over centuries. The remaining populations , like in Tibet, Xinjiang, and Yunnan, now live in remote areas with little access to commerce and capital flow. The one exception was the Manchus. During the Qing Dynasty, the Manchu rulers strictly controlled access to the Manchurian heartland in order to maintain the racial and natural purity of their homeland. They essentially wanted to cultivate their "Manchu" identity by keeping their connection to the natural. Mark Elliot's "The Manchu Way: The Eight Banners and Ethnic Identity in Late Imperial China" is a great book for learning more about this. My favorite book on this topic is Jonathan Schlesinger's "A world trimmed with fur : wild things, pristine places, and the natural fringes of Qing." The Qing rulers and banners slowly became more and more "Chinese," and lost their ability to speak the Manchu language. By the 19th century, the QIng emperors were wholly unable to speak their "native tongue," and their fertile and resource rich homeland was opened up to settlement. Today, there are virtually no Manchu speakers left.

Edit: I mistakenly said earlier that there are virtually now Manchus left, I meant to write that there virtually no Manchu language speakers left. My apologies.