Sifu:
In your photo, you are measuring the critical depth of the notch correctly, parallel to the member depth, square to the t&b edges; from 7.5" at bot. edge, to 6.25" at the reentrant corner, or 1.25" notch depth. I can about sketch on that photo how that member will split up its length, from the reentrant corner. The approx. 2x4 canti. out to the fascia is not as critical because its bending action tends to close a longitudinal crack or not cause one.
To understand the problem with that notched bearing, try this experiment: take a 2x4 - 3' or 4' long, at one end of the member cut a notch, thus; measure down from the top edge 1" and draw a line parallel to the top, in 2.5" from the end into the member, then draw a square line down to the bottom edge of the member. Cut the 2.5"x2.5" notch piece out of the member, but don’t over cut on either line or you just make the problem worse. Support this member on two sawhorses, one end bearing on the bottom edge and the other end bearing on the 1" remaining part of the member; this is a fairly good representation of your notched rafter. Load this member at the middle and it will split lengthwise, starting right at the reentrant corner, at a fairly low load, and very much dependant upon the grain orientation down the member length. On a new member cut the notch so 2" of material remains on the top (cut out is now 1.5"x2.5") the failure load and mechanism will be about the same. That’s the nature of this beast. If you now cut the notch so 3" of material remains on the top (cut out is now .5"x2.5") and if you put a generous radius at the reentrant corner this last member will start to act almost like a full depth 2x4. But, it will still likely split at less than full cap’y. because of the notch affect.
Your valley rafter has the same problem. Take a 2x4 and cut a 12" x 2.5" sloped seat cut on the end of it, like your valley rafter. Support this 1" from the end and load the member, it will split lengthwise, from the edge of the bearing surface. Support this right back at the heel, near the bottom edge and it will act like a full depth member.
When we write a prescriptive code, whatever it says exactly about notch depth, we have to be fairly conservative, because some users won’t have spent two hours in a college Structural Engineering class on wood design, on this exact topic. Furthermore, this problem is so sensitive to the wood grain and its orientation, that any notch might be a problem, and no notch is best.
You might want to send the guy a letter telling him he is going to be ripping out a bunch of his work, so you can do your framing inspection; and until you have the calcs. and details and explanations, signed and stamped by his engineer, he might be replacing some of the framing too. So, at this point he is working at his own risk, and may want to expedite his engineer’s certification of the existing conditions.