Does the treaty help a US citizen living in India?
It helps with the Indian side, and only partly with the American one. The treaty caps what India may withhold on certain income and allocates taxing rights between the two countries. It does not release a US citizen from filing in the United States, because American tax follows citizenship rather than residence. So the usual shape of the answer is that India taxes under the treaty, the United States taxes in any event, and the double charge is relieved by crediting Indian tax on the American return. The treaty is half the answer. Citizenship is the other half, and it does not go away.
Do I have to tell the IRS I am relying on a treaty position?
Sometimes, yes. Where a position depends on the treaty rather than on ordinary domestic law, the United States may require that reliance to be disclosed with the return rather than simply reflected in the figures. India separately wants its own declaration before an Indian payer will apply a treaty rate. So one treaty position can generate paperwork on both sides, with a document to obtain the rate in India and another to disclose the position in the United States. Treating the treaty as self-executing is what leaves one of those two unfiled, usually the American one.
Does the treaty override US citizenship-based taxation?
No. The treaty decides which country may tax what, and caps some Indian withholding rates. It does not change who the United States regards as taxable. A US citizen stays inside the American system regardless of where they live or what the treaty says about residence. The practical consequence is that the treaty rarely produces a nil result for a US citizen. It produces an ordering: India collects first on Indian-source income at the capped rate, the American return reports the same income, and credit for the Indian tax reduces the American charge on it.
Why did my Indian investment deduct tax when I already pay US tax?
Because India collects at source before considering any exemption or credit. The Indian payer has no way of knowing what you have paid or will pay in the United States, and it is not the payer's job to find out. It deducts at the domestic rate unless it has been given the declaration and certificate that entitle it to the treaty rate. What you pay in America is dealt with much later, on the American return, as credit for Indian tax borne. The two events can be a year or more apart, which is why one file has to track both.
Can I claim a US foreign tax credit for Indian tax withheld?
For Indian tax you were properly liable to, yes. For tax deducted above the treaty cap, that is a different question. An over-deduction is money India is holding which you can reclaim from India, and a credit claim built on it rests on an amount you were never obliged to bear. The orderly sequence is to establish the treaty entitlement, settle what India keeps, then claim that figure on the American return. The alternative is asking the United States to fund an Indian refund you have not applied for, which is not a position worth defending.
Which return do I file first, the Indian one or the US one?
It depends on which country has the primary taxing right over the income, and that is decided type by type under the treaty rather than once for the whole file. As a working rule, Indian-source income taxed at source in India is settled there first and credited in the United States afterwards. The complication is the year end. The two systems close their years on different dates, so tax India deducts in one of its years may belong against income reported in an American year that has already been filed.
Which country do I pay tax to first?
Generally the source country — where the income arises — taxes first, often by withholding before you receive it. Your country of residence then taxes the same income and credits what the source country took. That order is why timing matters: a residence-country return filed before the source-country tax is settled has nothing to credit yet. Getting the sequence right is most of the work. See international tax planning.
Do dual citizens pay taxes in both countries?
Both countries can have a claim, but paying double taxes on the same dollar is the exception rather than the rule. The United States taxes its citizens wherever they live; Canada, India and most others tax on residence. So a dual citizen living in one of them often files in both — a resident return in one, a citizen return in the other — while the credit and exclusion rules mean the total is usually close to the higher of the two, not the sum. Filing twice is not paying twice. See two returns as a dual citizen.