How on-sensor phase detection is accomplished varies somewhat. It can be pixels where the micro lenses are oriented in opposite directions. It can be multiple *pixels under a single micro lens with a baffle between them. And it can be partially masked pixels (but that example image isn't very good IMO).
And there's probably some arrangement yet to be designed or I don't know about; but they all work based on the converging virtual images as shown in your first two diagrams.
And you are right; however it is accomplished, when the left/right (or upper/lower) virtual images merge as a single focused image there is no longer a phase difference. At that point a mirrorless camera must switch to contrast detection for any changes/refinements. Of course, what is considered "focused" in this sense depends on the resolution of the sensor/size of the PDAF points. E.g. if the two virtual images are falling on two separate photodiodes, which are binned as a single pixel in the output, then they are maximally "in focus" (combined as a single image) even though there is still a separation.
And even if both virtual images are perfectly aligned that does not mean that the camera cannot monitor the PDAF focus points in order to detect when a phase difference reoccurs (and then correct for that).
On-sensor PDAF is very much the same as using a split prism viewfinder; when using a split prism viewfinder you can see when the left/right virtual images are not combined as a single image (in focus), you can see when they are, and you can see when they separate again. And likewise, the on-sensor PDAF is very dependent on the light/image falling on it just as the split prism is... this is all quite different from the DSLR's dedicated PDAF system (which uses multiple real images).
*they are now starting to distinguish the difference between photodiode/detector and pixel/picture element when multiple photosites are binned in the sensor output.
EDIT TO ADD
I found this good reference on the history of focusing in cameras. It covers the physics of using ground glass (diffused focus screen), rangefinders, split prisms (phase); and discusses their implementations into autofocus.