From the Austrian Fulbright Website FAQ about USTA section:
"
As a U.S. Teaching Assistant, am I a Fulbrighter?
No, because the U.S. Teaching Assistantship program is not part of the official Fulbright grant programs. The Fulbright Commission administers the program for the Austrian Federal Ministry for Education, Arts and Culture. As a U.S. Teaching Assistant you are a salaried employee of the respective local school board."
Can I apply to the U.S. Teaching Assistantship program in Austria if I also apply to a Fulbright ETA program in a different country?
Yes, because the Austrian U.S. Teaching Assistantship program is not part of the official Fulbright grant programs."
by the way, best of luck Eule! hope you get off the alternate list soon!
