Hm... That is a point, but even back then it must have been known that America was big big big, and the 13 colonies were a mere pinprik in it all. Of course it could have been a political agenda, in that they would call the citizens Americans to gather support among the rest of the colonies, even among foreign colonies. You know along the lines, "we are all Americans, they are all Europeans." But I have heard no such claims.

Personally I just believe the people who did it simply didn't think about it. "United States of America sounds good, don't you think Jefferson?" "Sure it does! And we should call ourselves Americans to make certain that those Brits know we are not like them, we are from another continent. We belong free." But not a single one considered the fact that there were millions more Americans out there, who would not belong in their state. A simple oversight.
Admittedly there was quite a bit of America outside of the U.S. But at least in the 18th and 19th centuries the U.S did spend a considerable amount of time trying to add at least most of (or perhaps all, if I recall correctly Seward wanted to conquer Canada and Mexico with the Union army for example) of N. America to the U.S.

By the 20th century American for citizen of the U.S. is really just an inculcated historical artifact. Nobody calls people from the Netherlands Netherlanders, but rather the Dutch (or maybe somebody does since MS Word actually corrected the word…).