It depends upon the context. Here in the U.S.A., someone from India is usually referred to as "Asian Indian," "East Indian," and "India Indian," to discern the difference from those often referred to as American Indians/Native Americans, i.e. the Aboriginal peoples of the Western Hemisphere and the native people who previously were the inhabitants of the region of North America that became the U.S.A. Native people of Alaska (e.g. Inuit, Tlingit, Tsimshiam, Haida, Aluet, Inupiaq, Yupik, etc.) are usually referred to as "Alaska Natives" but also are considered "Native Americans," as are Native Hawaiians but neither Alaska Natives nor Native Hawaiians are generally referred to as "American Indians" since they are not associated with the region of the contiguous 48 states of the U.S.A.
Historically, the British, the colonizing culprits in this whole mess (that's sarcasm folks, aka "Indi'n Humor), often referred in their literature to "Indians" as the people from the Indus River Valley, aka India; the people of North America, they often referred to as "Red Indians." Here in the U.S.A., the term "American Indians" is usually converted to a contraction and pronounced as "Indi'n" by many who are of American Indian/Native American descent or many of the people inhabiting areas with large populations of American Indians/Native Americans.
The whole, "use Native American to refer to American Indians," argument is often confusing (since anyone born within the confines of U.S. borders is often referred to as "Native Americans" rather than "Native Born Americans") and comes across in "Indi'n Country" as lip service, an often insincere term that is used by the mainstream to feign respect for the aboriginal people of the U.S.A. but is often used to marginalize and divert attention away from the issues that have historically evolved in the U.S., such as American Indian tribes' legal status and claims in regard to their interactions between the U.S. federal and state governments, usually defined by treaties and the U.S. Supreme Court who use the term "American Indian" in their copious discussions and documents on the legal status of American Indians.
I hope this clears up some of the discussion as to why most people who trace their ancestry back to the people of the Indus River Valley, aka India, are commonly referred to in the U.S.A. as "East Indians," "Asian Indians" and "India Indians," in an attempt to avoid confusion. I have no idea what people in India might call American Indians/Native Americans who travel to or reside in India. I would think they would identify them by their tribal names, such as Cherokee, Lakota, Leni Lenape/Delaware, Kiowa, Apache, etc., but that is total conjecture on my part.