I would presume that the name was later transferred to a single system and its planets (the same way "Indian" was transferred from residents of India to residents of North America) for whatever reason. Star Charts says it's a Member, and there's no reason that colony couldn't have grown into one.
Could I just clarify that people in India itself, and in quite a number of countries on Earth, do not go around referring to people from Mumbai or Goa as being 'East' Indian?
(And for that matter, there are places like Canada where terms like 'First Nations' are promoted in place of other, older, less geographically accurate terms used to describe those aboriginal peoples that are neither Inuit nor Métis...)
But then, upon reflection, I'm kind of hoping not to have just proved foravalon
's signature quote to be correct!