Attaching newel post to joist
You will need a box newel with a long enough bottom section to notch over the  joists and attach it to the sides of the joist, through the face of the box newel. Anchoring is superb this way. This will let the stair skirt board die into it, the box newel will extend to the floor and the nosings will butt into either face of the bow newel. This is thew way I do it, or would do it.... On the other hand....

Your details are pretty well defined already. This looks like a fabricator pre-assembled everything in a shop, connected to the white sole plate, set it in place and screwed it down. The sole plate is the strength of the whole system. I am not crazy about this type of install and if it were me, I would detail my anchoring style with the finish details you have established just to keep everything consistent. That would mean swapping out where the anchoring is done. Instead of screwing into theoutside face of the joists, I would cut the box newel so it would screw to the inside corner of the framing after the subfloor is cut out a bit.

If the box newels are not available that long at the bottom to do it this way, they are hollow that I am aware of, so set a proper sized solid 4X4 or 3X3 at the center where the newel will set, long enough to extend about 2 ft or so above the floor and drop the box newel over it after the white sole plate is in place. Glue and or nail in place.