This is a very difficult question to answer, one which has many factors pertaining to many of these nations which have very different histories. Nevertheless, I've tried to be as succinct as possible below.

The primary reason for the rapid economic rise of many of these nations directly after WW2 was the onset of the Cold War, and the overseeing and great encouragement of many of these economies by the United States, and to a lesser extent the British Empire.

So firstly I just want to clarify that it this was not down to acts of great philanthropy or charity on behalf of the US or the Empire, but rather these decisions were wholly strategic.

Before WW2 had concluded, there were many strategic choices made by Washington, London, and Moscow in order to best advance their post-war agendas and spheres of influence. In Europe, Stalin famously pitted two of his leading Marshals - Ivan Konev and Georgy Zhukov - in a 'Race to Berlin' due to a desire for the Soviets to capture the German capital instead of the capitalist allies of the West because he believed it would give him the upper hand in the post-war settlement of deciding Germany's fate. In South East Asia, similar strategic decisions were made by the US in disallowing any Soviet occupation of the Japanese Empire or the islands of Japan, despite the Russian entry late into the war in August 1945 being a considerable factor in the Japanese surrender. (Although the Soviet Union, in the event, did occupy the Kuril Islands until the end of the 40s, and was allocated North Korea which it didn't formally occupy.)

As the war concluded, its important to recognise that there was a desire on the part of the Europeans to return to the antebellum situation. Indochina was to return to French control. The British would keep hold of Burma, Singapore, Hong Kong and Malaysia. Korea, never under European control, was hastily divided along the 38th parallel with the Soviet 'sphere of influence' in the north, and the US' in the south.

With the deterioration of the relations between the Soviet Union and the capitalist and imperialist nations of Western Europe and North America (NATO wasn't formed until 1949), the United States in particular began to ramp up efforts to reenergise the economies of the nations they had been occupying since the end of the war. General MacArthur was effectively put in charge of post-war Japan, and the Americans heavily encouraged the Japanese to reorganise their economies, and began in the 1940s and 50s to focus heavily on producing resources like steel, coal and cotton which could find ample markets in the United States.

This was all rapidly encouraged by the onset of the Korean War, the first 'hot' flashpoint of the Cold War in the East. The US pumped large amounts of money into countries like South Korea and Japan, and provided the green light and assistance for a coup in South Korea by an aggressive capitalist administration in 1961 which wanted to focus on a top-down reorganisation of the economy, moving away from agrarian interests to foreign investment and giving huge tax breaks to large family conglomerates like Hyundai, LG and Samsung. The US donated billions of dollars to the South Korean government to assist this as well as to help in funding the South Korean military - ever attempting to at first 'contain' the spread of Communism, and then to 'roll it back' in places like Vietnam. This kind of economic assistance was given to Taiwan as well, which in the 1950s saw rapid economic growth due to huge reforms in the way land was used - large landowners were paid off of their lands which were used by state and private enterprise businesses focussed on industrial output. For much of the 1960s, many American goods were made in Taiwan just as they are in mainland China today.

A lot of this aid American was cut back by the 1970s, but still played a huge part in financing the armed forces of these countries due to the perceived threat of communism from the Soviet Union and, later, China.

Regarding Singapore and Hong Kong, the story is a little different. Both were British colonies at the end of the war and the US had less direct involvement in this British 'sphere', yet the British state had barely enough money to fund itself let alone provide economic support to the colonies it had spent the better part of 150 years extracting wealth from. In 1947, the British informed the US government they could no longer fund the military support for Greece and Turkey, for example, and had to ask for the US to take over.

Singapore grew consistently from the late 1950s, after independence, through similar models of restructuring a very agrarian economy to one of manufacturing and trade (it had always been a strong trading outpost) and, more importantly, services. Singapore quickly developed a reputation as the centre of banking in South East Asia, one it holds to this day. This, combined with notoriously low taxes began to attract businesses from abroad, especially in the US and Western Europe.

Hong Kong is an altogether different story, held in the famous 99-year lease by the British until 1997. It proved a vitally important sector for the British in Asia, being for a very long time the only part of the Chinese market that was open to foreign investment. Huge multinational businesses such as HSBC had a home there, and the colony grew on its reputation and reality of a commercial and trading hub from the late C19th onwards. After the Chinese Communist Party swept to power at the end of the Civil War in 1949, millions of refugees fled from the mainland to HK and Taiwan (and millions more to Europe and the US). This produced a swathe of labour which allowed for the manufacturing of cheap, exportable goods which slowly developed into national businesses through government incentives.

Yet even this was within the confines of the Cold War. While decolonisation was occurring in Africa and Asia, the British were firm in holding onto Hong Kong because of its economic assets, but also its strategic positioning as a free-market entrance into China. The US backed this resolutely.

As for China, that story is far more recent. The slow opening up of the CCP to foreign investment after the death of Mao throughout the 80s and 90s has led to an economic growth the world hasn't seen the likes of before. A centralised government with a top-down approach to economics and over a billion people at their disposal; China is on a seemingly exponential rise which may only be halted by the ruminations of civil unrest.