USian is a term adopted by English speakers who wish to more clearly distinguish between things related to the United States (the political entity), and things related to the Americas (the geographical entity(ies)). Motivations can range from a desire for precision in speech to a recognition that claiming the term "America" for one country, when in fact it is two continents with dozens of countries, isn't terribly considerate. People from Canada, Mexico, and Chile can all legitimately say they are "American", just like both Germans and Spaniards are "European", but using the term extensively to mean "people or matters related to the US" makes this less viable.
Note that in Spanish the term Estadounidense (note the similarity to "Estados Unidos") exists, though I don't know how much it's used.
Of course, it's an uphill battle, especially when you consider that the official name for Mexico is Estados Unidos Mexicanos.
> The point is that saying someone or something is "American" shouldn't cause one to assume it's from or of the US.
That's seems like it's a pretty silly sentiment, since in common English speech that's exactly what 'American' implies.
As you yourself note, USian could just as easily refer to someone from the United States of Mexico.
I personally think it'd be salutary for our republic if my fellow Americans would refer to themselves as New Yorkers, Californians, Georgians, Texans &c. rather than as Americans (just as Germans, French, Dutch, Danish refer to themselves), but that's a different discussion altogether.
I actually prefer to call myself Californian in most contexts. I also think the word "state" is diluted by the US.
Anyway, I'm not really advocating for one side or the other. In common usage "American" definitely relates to the US most of the time.
I can understand the annoyance of people from other American countries, though. Surely Nigerians, Eritreans, etc. would have a reason to be frustrated if "African" came to refer particularly to "South Africa" and not to the continent.
I think that's a perfectly reasonable assumption, since it's by far the most common usage of the term. If someone uses the term "American" to mean "person from the Americas" they are being needlessly obtuse.
And I don't think this usage is particularly "inconsiderate", it's just a quirk of language.
Note that in Spanish the term Estadounidense (note the similarity to "Estados Unidos") exists, though I don't know how much it's used.
Of course, it's an uphill battle, especially when you consider that the official name for Mexico is Estados Unidos Mexicanos.