Those nations that you listed accepted hundreds of thousands of Europeans, over the last 400 years. When Jews fled Spain in the 16th century, they went to Turkey. The reason large numbers of Asians didn't move to Europe was that it was a largely poor continent. Countries like Spain, Portugal, Italy, Greece, etc were poor even in the first half of the 20th century.

The reason that Asians didn't move to the more prosperous Americas till the 1960s was the racist immigration policy in the US and Canada, which prevented Asians from coming in. 

As far as I know, no race or nationality is singled out for discrimination in Asia. It is equally hard for everyone! However, India has over 15 million Bangladeshi immigrants, and probably a million Nepalis too. Jordan has millions of Iraqi and Syrian refugees. Turkey has millions of Syrian refugees. Thailand has millions of Burmese and Cambodian immigrants. Malaysia has millions of Bangladeshi, Indonesian and Filipino immigrants.