There might be as many people from Pakistan, East Africa, or China who have to migrate because of global warming this winter too. Not sure whether they’ll go to Europe, but millions isn’t an exaggeration in those cases.
China is too big of a territory; if the Chinese needed to migrate because of global warming, they'd likely move within their own land. Probably the same case with Pakistan.
Pakistan is already exploding at the seams due to population growth. It's not just a matter of moving, the country doesn't have enough resources to feed and clothe its population. The growth rate isn't abating and global warming is eating into water resources and desertifying land / reducing the arable area.