Need banking advice for Venice

Yes, I believe that is correct. No ATMs at the train station last we were there (October). Do it at the airport.

The map of the airport arrivals level shows an ATM machine inside the luggage claim area and another just past the exit gate. It is Symbol A on the schematic map:
http://www.veniceairport.it/en/at-the-airport/terminal-maps.html

By "the train station" are you referring to Mestre or Santa Lucia?

Ah, I meant Mestre.

There are also ATMs located at several vaporetto stops along the G
Canal.

Edit: didn't catch Austria.

If you are heading to Austria from Mestre you will not be near a vaporetto. I've never had an issue with the ATM's at the airport. Two by the luggage carousels, which you can use while waiting for your bags to show up on the belt, and one after you exit the green door. If, for some reason that doesn't work, there are banks about a quarter mile north of Mestre station if you have time, but I don't think you will need them.

Perfect, we will use the ones near the luggage carousel.

Just make sure you use bank ATM's and not "convenience" ones as you'll lose about 5% on the transaction.

My experience, no issues with ATM's at Venice Airport, and I always put on my green eye shades when I get home and figure what actual exchange rate I got.