Canada’s white paper explains that, wherever cloud resources are physically located, stored data may be subject to the laws of other countries, because a provider with foreign operations could be required to comply with a warrant, court order or subpoena from a foreign law-enforcement agency. In its 2018 analysis the paper names the US Foreign Intelligence Surveillance Act as the primary risk to data sovereignty.
A concrete statute is 18 U.S.C. § 2713, added in March 2018 by Public Law 115-141, division V, the law known as the CLOUD Act. It requires providers of electronic communication or remote computing services to comply with preservation and disclosure obligations for data in their possession, custody or control, whether the data is located inside or outside the United States.
The point is general rather than American. A provider that operates in a country can be bound by that country’s law, and the same holds for Indian authorities and providers operating in India. The practical question is which jurisdictions your provider, its parent company and its sub-processors answer to.