Sky Dome and ambient illumination are not HDRI. HDRI means "high dynamic range illumination" that means any light or illumination scheme that use intensity ranges that are beyond the 256 possible values fora color with the 24 bit RGB colors.
You can map a sky dome with a normal or HDRI texture, but it is nothing more than a background sky image, it doesn't illuminate the scene.
To have a scene illuminated by the light comming from the atmosphere you need something more.
There are many solutions to the problem. One is to use a physically based illumination model taking into account the scatering of the atmosphere.
Another  aproach is to map a sphere with a texture, the mathematics involved are very simple, but you need special textures and a special light source.
First at all, one sphere is not enough, you need two spheres. If you look at the sky you see that is blue, but you are not illuminated by a blue color!
If you use a sphere painted with a blue gradient and use this sphere as a filter your scene will be blue, what is wrong!
So you need two spheres, one with blue color that doesn't act as a filter and only will give you a background image of the sky and the other sphere that will act only as filter for the incoming light, but without  any illumination visible on this sphere. This time the texture has to be with orange-yellow colors depending on the position of the sun.
As for the light source you need a special omnidirectional convergent light, a light that comes from outside in all directions and converge toward the center of the sphere.
This kind of light is, of course, not available in Poser and any array of spot lights will fail to produce the desired effect.

Stupidity also evolves!