Where are you actually trying to go?
Testing at airports is not relevant to needing to quarantine or not.
In most EU states it is unlikely they will check on you during your quarantine but I have heard a few cases of random inspections. The key is to remember that the quarantine requirement will likely vary by country. For example, if you connect to VIE, then leave Austria, Austrian rules are no longer valid. If someone stops you and sees that you entered the EU (or more realistically, departed a non-EU country) during the last 14 days you could have issues - this could be detected on intra-Schengen flights for example. The worst-case would be if you actually had the virus and got discovered, then you’d be in all sorts of issues as most countries now require written health declarations that include travel history upon entering even from within the EU, including Spain.
According to AT embassy:
2.2 ENTRY FROM WITHIN THE EU, THE SCHENGEN AREA, SELECT SMALL EUROPEAN NATIONS AND THE UNITED KINGDOM:
Individuals wanting to enter Austria from a EU member state, the Schengen Area, or from Andorra, Monaco, San Marino, the Vatican, or the United Kingdom
must present a medical certificate confirming a negative molecular-biological SARS-CoV-2 test no older than four days at the time of entry (certificate in
German /
English).
Individuals who cannot provide such a certificate will have to quarantine for 14 days at home (self-monitored) or at an appropriate accommodation which must not be left for the duration of the quarantine.
A negative molecular-biological test conducted and presented during the quarantine will end it and the location can be left. Individuals are responsible for covering the cost of the quarantine accommodation;
at the time of entry a confirmation of the availability of such an accommodation to the individual must be presented, otherwise entry will be denied.
Individuals transiting Austria without stop are not subject to the above entry restrictions.
Individuals who enter Austria coming from one of the following states and have their residence in Austria or one of the following states:
Andorra, Belgium, Bulgaria, Denmark, Germany, Estonia, Finland, France, Greece, Ireland, Iceland, Italy, Croatia, Latvia, Liechtenstein, Lithuania. Luxembourg, Malta, Monaco, The Netherlands, Norway, Poland, Romania, San Marino, Switzerland, Slovakia, Slovenia, Spain, Czech Republic, Hungary, Vatican, Cyprus
do not have to present the medical certificate and are not subject to a quarantine
if they can credibly show that they were not present in any other state than Austria and the states listed above within the last 14 days.