You could not be further from the truth. Carbon emissions per capita is way higher in the US and in Europe than in China and India.
However the other important factor here is the trend line. Most western countries above China in this ranking has a trend line pointing downwards, while China still has a trend line pointing upwards. So if both China and the US continue on their current paths then China will indeed soon surpass the US.
It would seem that manufacturing would have a significant impact on the figures and a lot of manufacturing has been outsourced to China/India.
So how much of all the stuff that is bought and consumed in the EU/USA is actually produced in China or India?
Source: https://en.wikipedia.org/wiki/List_of_countries_by_carbon_di...
That same article lists the EU overall at 8.6 and US at 17.