Looking at the file again I see that the rivet’s is not in the same place as the plane’s origin. That just offsets all of rivets unidirectionally. Maybe I should’ve explained that better in the video: any transform on the instanced object you have relative to the instancer is taken into account. This is why, for example, you had the issue of rivets rotating before.
Now, I think (this is off the top of my head right now) you may avoid some of these problems if, when parenting the rivet to the instancer, you choose to parent ‘Without Inverse’, as that should negate the transform differences. Then you’ll basically only need to make sure that the rivet, in its default orientation, has its Z axis pointing up (i.e. out from the rivet).
As for the curve, keep in mind that you have the Shrinkwrap after the Curve modifier, it might reposition the planes even if you adjust a curve slightly.
