The Profoto Deep umbrellas are NOT truly parabolic. Most other so-called parabolic umbrellas and softboxes are not truly parabolic either. This has various reasons:
The focus point of a deep parabola is close to its vertex. Closer than the inner rods of an umbrella need to be for the umbrella to stay open. That means however, that the light source cannot be moved into the focus point because these inner rods are in the way. Manufacturers deal with this in two ways: some manufacturers (like Buff) make their umbrellas shallow. This moves the focus point further out so they can be focused, however spill becomes a problem. Other manufacturers (like Profoto) make their umbrellas deep but not parabolic. The Profoto compromise is not bad. While nothing like a Briese or Bron, it can be focused quite nicely and it's light and affordable. But (even when focused) the light from these umbrellas is not parallel.
There are other, mechanical, reasons that make parabolic reflectors a challenge. This is why most so-called parabolic
softboxes (not umbrellas) are not truly parabolic either. I examined this and wrote more about it in my blog article where I also compared 3 "parabolic" softboxes:
Comparing parabolic softboxes for focusable reflector.
I have also written an article about
Calculating parabolic reflectors. That article includes a little calculator utility which runs in the browser and allows you to calculate the shape of a reflector from some key parameters such as diameter and depth. If you enter the dimensions of your favorite "parabolic" reflector, you can see what it SHOULD have looked like if it was truly parabolic.