during the british Empire did Englishmen living in India, etc. call themselves Indians, South Africans, Australians.....or Englishmen

It may be illogical and not strictly accurate, but I have no real problem with Americans=US'ns in common parlance. In that sense, Americans are also North Americans (but not necessarily vice versa), but not South Americans. Of course if one was discussing North and South and whole American continents, one would probably avoid the term.

But Whitman, I am not sure how your question above relates to the argument about what US citizens are called. Most (male) people living for a while in a country still refer to themselves as "an X-man living in Y-land". And in those times, the longer stay colonists still thought of themselves as "X-men". Or were you alluding to the confusion between Britain and England? I'm confused myself as to what you meant so can't start throwing rocks (yet )