How did imperialism in Asia help Asia?

In a post medievial society imperialism helped. The king, the Tsar or the Emperor was the sole governing authority. Inherited positions. General people had no say. The counsellors to the Emperor played active roles. This was upto 2nd world war. Monarchies in Europe even before great world wars changed a little. They allowed some civil rights and some form or portion of public democracy. Its the Great October Revolution in 1917 in Russia and defeat of Germany in WWII changed all.
Asian Imperialists
As fellow expert Chuck Siata notes, the primary benefits of imperialism accrued to the imperialist countries and Asia was primarily a victim of imperialism. The only imperialist country in Asia was Japan. Japan did modernize and acquire vast amounts of resources and labor by taking raw materials from both Korea and northern China and by forcibly conscripting Koreans into the Japanese Army and the Japanese industrial complex (the zaibatsu).

Asian Colonies
As concerns the remainder of Asia, which was subject to imperialism, but not containing imperialist powers, e.g. the colonies, there were three major benefits which accrued to these countries.

1) Institutional Protection for Minorities: The prior kingdoms, empires, and autocracies throughout Asia, such as the Mughal Empire, the Qing Empire, the Nguyen Kingdom, and several others, were states that privileged a specific ethnic or religious group above all others. This group was typically the majority, with the one exception being the Mughals, where Hindus were the majority but Muslims were the privileged class. The imperialists forcibly equated all of the different groups, making the majority and minorities on par. This led to many of these minorities supporting the imperialists, who served as their guarantors. In the post-imperialist period, a number of these minorities have managed to maintain a good position while others have been less lucky.

2) Infrastructure Developments: Imperialists built numerous forms of infrastructure in the colonial countries, such as railroads, universities, hospitals, bridges, roads, plumbing, electricity, and numerous other forms of infrastructure. Many of these elements are still present in the former colonies and remain key elements of those countries' modern infrastructure.

3) Military Organization: The Imperialists generally ruled the colonies by using locally organized armies and militias, meaning that local colonists would be those who received key military training. Upon independence, it was former colonial armed leaders who were able to lead the defense of the newly independent countries, often by defecting to whatever revolutionary group was fighting for independence.
Imperialism by powerful nations against weaker Asian nations was a benefit for the aggressive imperialists. The only people in the weaker nations that might gain from an outside imperial army, would be weaker nation people who might accept bribes for helping out the imperialists. This was risky however. Risky in that their imperialist "friends" could against them at any time, and/or the native peoples under imperial oppression might turn violently against the traitors. Asia was a victim of powerful European powers, Imperial Japanese forces and even the USA.