How long can a population grow once it has reached the replacement fertility rate? The Ministry of Health and Family Welfare answered in the upper house to a question that India has a fertility rate of 2.2 (link here). The replacement fertility level is usually given at 2.1 to 2.2. 

These sources suggest that India's population is projected to grow at least until 2060 (2050 in some sources): Quartz, The Hindu. 

The Quartz article even cits UN population projects and says: 


  Even under the instant-replacement fertility variant, with the country’s fertility assumed to fall immediately to 2.1 births per woman, India’s population would reach 1.9 billion by the century’s close.


This source defines the replacement fertility level as: 


  Replacement level fertility is the level of fertility at which a population exactly replaces itself from one generation to the next. In developed countries, replacement level fertility can be taken as requiring an average of 2.1 children per woman.


What I don't understand is: how can India's population be projected to grow until 2060 if it has already reached replacement fertility level in 2017? A 'generation' is usually 25 years. Even if we take it as 30 years, India's population should stop growing in a couple of decades. How does the UN project that it'll grow until 2060?
Population size isn't just about birth rate.

It's also about death rate and net migration.

If the health of India's population continues to improve, then life expectancy will increase, and population size will continue to grow until life expectancy stops increasing, assuming zero net migration.

Net inward migration would also increase the population size.