Hello from Greece! Ok so on the plane before the app is ready on 1 July, you fill out one of two forms, the naughty orange one for bad countries origination (I had to fill it out, they knew from my seat number and name that I had connected in ZRH from LHR) and the blue one for the good countries list. What is funny is even though I filled out the orange naughty form and gave it to the cabin crew, I got off the plane without being tested and simply went to pick up my luggage and off to do as I please. So they do not test all arrivals, even if you are not from a 'clean country'. This is something I suspected; they simply do not have the infastructure to test every arrival who connects from a 'good country' even though they originate from a 'bad country'.
The highest chance of getting tested upon arrival is if you directly fly in to Greece from a 'hotspot', if you connect through Switzerland or Germany, it is much less likely you will get tested, but I am sure the authorities are aware of that and this is why they created the app, so let's see what happens after July 1.