There's "three" ways to get volumetrics into your scene (for this kind of effect).
- Encapsulating your scene in a "domain" (like a cube). The material of the object should be Specular, with Index 1 and Fake Shadows (If you want to use "external light", like environment texture/daylight) and then with a Volume Medium node connected. The problem is that the camera have to be outside of the "domain"*.
- Encapsulate your camera with a "domain", but with inverted normals. The material settings should be the same for #1. This essentially makes the rest of the world into a "volume domain", so the volume is (in theory) infinite (which perhaps isn't the most optimal).
The problem with these two are that they don't do well with animation because you have to keep the domain "outside" of the camera. This can create a visible border, and it also makes it harder to use in an animation (as you've noted).
What you can do is to parent he domain to the camera (mostly for #2) and reduce the Start Clipping to something like 1cm (or 1mm, depending on your needs) and then move your camera closer to the domain (for #1) or set the radius of the domain (for #2) to just slightly larger than the clipping start (you should be able to see the sphere/domain in the Blender camera view [and it should cover the whole f.o.v.])
- Using the Medium input/texture of the Octane Environment. This is my preferred method, since there is no need to fiddle around with domains etc.
Just create a world texture and connect a Volume Medium node to the "Output color"(!), then select that texture for Medium in the Environment settings.
You probably need to increase the "Medium Size" to cover your scene.
This is basically the same as #2, but with an "outer sphere/limit", and less hassle (no extra objects needed etc).
ETA: I used 4.02.1, but I exported the scene and opened it with 3.08 and it worked fine.
After that, you just need to fiddle around with the settings a bit (and make sure you're using Path tracing), I did some quick tests (bellow) with the volume settings you see in the screen shots.
(NB: There is some visual differences between the methods, but you only think about it when you look at them side by side)
(Top to bottom: Methods #3, #1, #2)
(* Unless I'm missing something. I looked at tutorials for C4D+Octane and it seems that they have the camera inside the volume, but I can't get that to work.)