As someone who has travelled somewhat in Asia, it's two things.

The developed countries in Asia already had facemasks because they were used to doing this. Generally, the idea "Society can't tell me what to do," just isn't a thing in Asia. So people cooperated on public health measures.

The second is underreporting. Don't get me wrong - a lot of developing countries are honest in their reporting, but it's simply the case that a lot of people fall between the cracks, even when there isn't an epidemic.