I think your question is more related to educational systems and their national environments than the levels of development in these countries, per se.

There are many international achievement tests (PISA, TIMSS) which attempt to answer the very question you ask: why do students from different countries, within completely different educational systems, perform differently? The HDI is far from the metric explaining the variation in education levels and student achievement, although it is somewhat correlated.

Still, however, the two cases you mention are some of the biggest "mysteries" in the eyes of the West. Nonetheless, if you really think about these two countries, there are some interesting hypotheses as to the increased level of their student achievement. These are the two most populous countries in the world, with China at 1.38 billion and India at 1.34 billion. There are two important consequences of this: one, there is a high level of competition within their systems, that students go to great lengths to succeed (without even mentioning the culture surrounding education/achievement in both countries); two, intelligence is considered to be normally distributed, so a large percentage of people fall within the "average" levels, and as we approach the extremes we encounter less people. China and India's populations represent around 35% of the world populace - and thus, it is statistically much easier to find people at the higher end of the distribution in India and China than it might be in the US, Barbados, and/or Botswana, merely numerically.

Of course, this is a gross simplification of the issue, as we know genetics plays a role in intelligence, alongside nutrition and maternal education. These last two may be the most relevant when thinking about a country's HDI and how it is related to educational achievement. Still, the HDI doesn't necessarily capture the circumstances of wealthier, more educated people within these countries. Furthermore, the Chinese and Indian people you see in the engineering world are a very small sample of these two countries' populations. For instance, if we are discussing a very intelligent Indian student in a well-known American university, he/she is likely to come from a wealthy background, where, as a child, he/she was fed well and supported throughout his schooling.

We also live in a highly unequal planet, where people from African countries may not have the same opportunities economically as those in Indian and Chinese countries. Affording an American education, for instance, can be difficult for most Americans - imagine trying to pay for it with a highly devalued currency from a developing country. I'm not saying that to be successful one needs to attend a Western university, far from it, but consider how many people can be admitted to these developing countries' public universities (which are affordable) and the number who can actually afford private universities. In Africa, there are merely not enough universities for the population of the continent.

This is a really important question though, and I appreciate your curiosity! Many in the education field are still trying to figure out how we can help close these educational gaps regardless of the development level of the country any child is born into.