OK so what happened is that after my home router got a firmware update _and_ I went and picked up the cameras to reset them, those that were pointing outside of the window, I got a notification. It said my face was identified and then I saw the recording in the camera timeline.
Two things: 1) it may be that there was something wrong in the router and the update helped. 2) I am stupid enough not to understand that Eve indoor cams do not detect movement through the window.
Eve Home do state this fact on their camera support page in the FAQ list. In the product description they do only discuss pointing the cam inside the home and using motion detection there. I could not find that they would explicitly say in product description - for stupid persons like me - that the cam does not detect movement through the window.
So just packaged the cams and will return them to Apple Store, since it is less than two weeks since I bought them. Case closed for me.