How to connect backyard cover to existing roof?
The photo does indeed show the patio cover extending up over the existing roof. This is not the normal way to do this sort of thing but apparently had to be done that way because there was next to no clearance between the tops of the windows and the existing roof overhang to attach a more conventional ledger board onto the side of the house. With the conventional ledger board it would be screwed into the wall studs and then the rafters of the patio cover would attach to the ledger using hanger brackets.

Using the method showing in the picture it is necessary to open up the existing roof covering so that the upper ends of the cover rafters can be tapered and fastened down to the roof structure. The the roofing material of the cover is installed followed by replacement covering of the existing roof overlapping the upper end of the cover material. Sometimes the cover rafters may even be extended and nailed to the sides of the existing roof rafters. Doing this requires removing the sheathing of the existing roof at the point where the join is made.

In that picture, the roof of the house is so flat that it is possible that they extended the roofing material of the patio cover all the way to the ridge of the house roof.