It seems to me that when I was younger "Asia" specifically referred to the far east, China, Japan, Korea etc whereas now it specifically refers to Pakistan.
I am not sure why this has come about, although I'm certain the panel will have some opinions.
Asia originally referred to Anatolia (now known as Asia Minor), the Europeans later used this term to describe anything east of Europe.
I have an Atlas from the 1930s, in it, pre-partition British India is clearly in Asia. The understand of what is or is not Asia hasn't changed since then.
What has changed is that we now have large numbers of South Asians living in the UK, for obvious reasons, Pakistanis etc don't care to be referred to as "Indian" hence the term is usually used to mean "Desi" (the South Asian term for themselves collectively).
In the US, there are a lot of East Asians but relatively speaking few South Asians and thus the term is more commonly used to refer to those of Chinese, Korean or Japanese descent e.g. Asian-Americans.