Yep that is true. Yuan that is Mongols are considered Chinese. This did not only apply to Islamic world but other Buddhist nations as well. And the Mughal in India are Mongols but was considered Indians.
In other words.
Assimilation happened to the Mongols.
India started small in the beginning. Then they began to conquer neighbor tribes and nations.
There is such thing as 100% pure Indians. Because Indians breed with many different tribes and nations that they conquered.
And because I do not want this to become a islam vs hindu topic.
I am gonna be fair with you. The Muslims did the same as the Indians.