U.S. citizens in possession of a valid U.S.-passport do not need a visa if traveling
to Austria as a tourist for a period not to exceed 90 days (visa waiver program).
We're not traveling as tourists, strictly speaking.
The same situation exists with Americans entering Canada, believe it or not. If you're American and enter Canada to do commercial business (i.e. you're selling stuff, or you're being paid by a Canadian firm, etc.) you need a Canadian work permit. I used to cross the border for work quite often (American employee of Canadian firm) and usually said that I was attending an academic conference, which did the trick.
Melinda