Thank you rvdborgt for your answer.So,Have you actually done this ‘going from Salzburg to Innsbruck pass through Germany,and useing the Eurail Austria Pass’ ?
Yes. All non-stop trains (RJX from ÖBB or Westbahn services) through that bit of Germany are operated by Austrian companies and Austrian tickets are 100% valid.
This corridor is in place for more than a century as it's a huge shortcut between Innsbruck and Salzburg.
You don't pass through customs or anything, it's like travelling in the same country.