Hi and welcome. Don't know what tools you have yet, so here goes.
I think it is far easier to cut a mortise at 90 degrees to the surface of the leg. Easier to hog out and shape the recess that way. The tennon, then, has to be cut as shown, at the same angle as the end pieces, but still 90 to the angled end cut.
I would make a pattern out of card stock first, with the angles laid out. Draw the tennon first, then use it to mark the location of the mortise on the leg pattern piece.
The challenge will be cutting the long grain piece to the correct angle. There are several ways to do that, most easily on a band saw, then hand work with a chisel to get it just right. If you don't have a band saw to work with, then I suggest getting a Japanese Dozuki hand saw. It is wicked sharp, but because it cuts on the pull stroke,it is easily controlled and very precise. To increase accuracy, while holding the handle, place your index finger on the side of the blade. It will reduce side movement of the blade--same as controlling a chef's knife.
To remove the shoulders, if you have a table saw, you will have to use your miter gauge and a flat top tooth blade set to a precise height (or a Dado set). The miter gauge will have to be set to the exact angle of the stool's splay. Take multiple passes to shave the tennon to the size you want, but it is almost always a good idea to have the tennon 3/8ths or so to make it easier to drill out the mortise. Leave just a little extra thickness (1/16th or so) so you can use some sandpaper or a chisel or hand plane to fit it to the mortise.
Mark the location of the mortise using the pattern, then carry the mark around to the narrow dimension of the board. Now you can use a drill press if you have one, to hog out the length and width of the mortise. If you don't have a drill press, you might try it with a drill guide of some sort. You could also use a plunge router, by sandwiching the leg in a number of thicknesses of scrap wood, to give you a flat surface for the router to ride on. Drill 3/8ths holes a little deeper than the tennon is long, then use a chisel to carve away until the sides are straight. You chisel must be ultra sharp. If you can't shave hair off your arm easily, it is not sharp enough.
The inside walls of the mortise should be flat and as smooth as possible.
Next, you will shave the sides of the tennon to make a snug fit in the tennon. Once it fits snugly (without forcing it in place), apply glue to both mortise and tennon and press them together. I would do this last, and I'd number both mortise and tennon so during glue up, you don't get confused about what goes where. Remember, each joint is custom fitted.
I am not familiar with the setup you have, but these are some options. If the jig will do any of these tasks, use it. But for me, the basic answer to your question is to allow the tennon to look like the drawing. Easier to cut the tennon angle than the mortise. And all the strength will be from the glue. I'd use some extended open glue. and be careful that the clamps don't throw the stool's structure out of square.
That's my opinion anyhow.
The more I do, the less I accomplish.
Last edited by DesertRatTom; 01-23-2019 at 12:07 PM.