I think we have to be careful about understanding the difference between nationality and citizenship; the two words should not be thought of as interchangeable although, unfortunately, many authorities do just that! I agree with Maureen that a child born in a British-administered area of India in 1893 would have acquired British nationality by virtue of being born wthin British territory, because nationality is a territorial concept. However, I am not convinced that such a child would have been deemed a "British citizen" and enjoy the "rights" of British citizenship, such as residence in the United Kingdom and electoral franchise. Citizenship is a political concept rather than a territorial one. The laws for the UK have been changed many times, as pointed out in the Wikipedia article, and 1893 falls between 1870 and 1914; various changes were made in both years. Annoyingly, the Wikipedia article also brings in the concept of being a "British subject", and this is covered in another Wikipedia article at https://en.wikipedia.org/wiki/British_subject. See also https://en.wikipedia.org/wiki/Citizenship. At this stage I'm not convinced that there is a simple answer to your question.