Maybe just try changing between the point types on your XSpline - say change to a corner and then back again to B-Spline. Who knows, it might refresh whatever math is happening to make those points do that? That one screenshot looks like the lines are being made based on the control points - so perhaps they are being treated as corners or with a very tight curve setting to them.
Also, since the tracking is applied to the Layers Matrix and not the shape itself you can merely hide your XSpline and then redraw the shape with a new B-spline inside the Nose Layer and it should follow the object you tracked just as well as what you have (the extra effort will obviously come with the other hand animations that need to be done when roto-ing something like nose movement).
I also took a look for 5 minutes and downloaded your project file and it made a perfect curve shape along the line for me, so your issue is indeed very strange. I did notice that when I zoom in to 1000% like your first screenshots then I start to see straight lined style stair stepping of aliased shape but I don’t think someone would see anything that is closer than 200% especially once motion blur is applied and matched.