More than one variable contributes to the effect in my experience.
If you look at this particular photo you’ll see that at least three things appear to be supporting the curvature of the collar, apart from the collar geometry itself:
(1) the jacket collar and lapel are holding it in that position;
(2) the tie blade is pushed up to the top of the collar band;
(3) the knot isn't small.
No doubt the geometry of the collar is a necessary condition, but I’m not sure it’s sufficient. Keep in mind that even a so-called ‘stiff’ collar band is still a somewhat flexible thing. Having a high enough band could be more important than its stiffness.
I suppose one could use a curved collar stay to ensure the effect, but I can't say for sure as I don't use collar stays.
As for the height of the collar band, that's what I thought as well at first. But I have a collar with front collar band height that's only 1", and I still have that effect. I'd take a picture if I hadn't sent it to Luxire already to be replicated. The shirt's collar features a rather short collar band (1" front and 1,5" back) that is unfused, but rather thick. It's actually from TM Lewin.
You need the make the collar height higher, the collar will stand.
Further, to make your collar stand nicer, you need to control the collar spread. You can measure the spread for the collar you like, and tell your tailor. If they can't control the spread, find another one who knows the tricks.