They cook a whole lot, for a variety of reasons. Many of these countries are less wealthy (can't speak to some of the wealthier countries like Singapore), and many have multigenerational households, where other generations help with household responsibilities, among other things.

As an aside, it's also interesting how big a difference the home-cuisine is versus what you may think of as that cuisine in many cases. I like to point at The Key to Chinese Cooking (https://www.amazon.com/Key-Chinese-Cooking-Irene-Kuo/dp/0394...) as a starting point for something more akin to Chinese home cuisine.