If you're talking about South Asians in particular then the fact is that most of them are not short, the SA in this country have concentrated origins from just a handful of cities/areas in their home country - you don't have an accurate representation of the whole Asian population in general, so you can only make assumptions of Asians from those few areas of their home country. India for example is a huge Asian country but there isn't proportionate emigration from the entire span of India more so Indian migrants come from a few hotspots of which the people may have genetic height similarities making them all seem shorter to you.
South Asians in general are very mixed race people and there is a quite vast array of height variances from one part of India to the other for example, and the same goes for Bangladesh and Pakistan etc. Of course if you check the averages (which aren't completely accurate tbh but do have merit) Asian populations definitely can't compare to Nordic ones like Sweden for example, those people are very tall, but they can compare with the English and Caucasian American population of today.
East Asian countries (not South East Asian e.g Philippines, Malaysia etc.) on the other hand are considerably less mixed race and are for the most part shorter than many other populations across the world. You should hold your horses though, because height increases in East Asia have and are being tracked in the past decade and populations in countries such as Japan and South Korea have experienced increased gains in height throughout the generations, there are even predictions that South Koreans may overtake many western countries in terms of average height.
The reasons for these gains are not clear cut but there have been reasons such as higher quality and more accessibility to nutritious food, advancement in medicine and better hygiene standards decreasing spread of disease stated among others. China is interesting as they have groups that are distinct in Northern China from those in Southern China, there are ethnic groups in Northern China that are very tall (6'1+) on average whilst other ethnic groups in Southern China are some of the shortest in the world. To answer your question in summary: you do not have the data to make the generalisation you did, your observation is not incorrect though, it is your subjective experience of the world around you. Posting on anon as I'm not interested in having a back and forth with any user, be it either malicious or productive, I just want to inform the OP even though I think there was no point in writing this in hindsight as people will see this as quickly forgotten fast-food information which is not wrong of them.