Trademarks are territorial in nature, which means that a trademark registered in India will be valid only within the territory of India. It does not provide protection outside of India.
However, as you mentioned, some countries do recognize and allow for the use of an Indian trademark registration as a basis for registering a trademark in their country. This is typically done through the use of international treaties and agreements, such as the Madrid Protocol, which allows for the international registration of trademarks based on a single application filed with the World Intellectual Property Organization (WIPO).
In such cases, the Indian trademark registration can be used as a basis for filing an international trademark application under the Madrid Protocol, which allows for the registration of trademarks in multiple countries using a single application. This can be a cost-effective and efficient way for trademark owners to obtain protection for their trademarks in multiple countries.