Yep, 2 cents from me, for clarity:
It was always like that in all versions of Corona before current V10 daily builds. You can easily check it by installing an older Corona version. 
It is a “bug” or an “unexpected behavior”, but now it is fixed and will be a part of Corona 10 release.
The other option is to use the “Inside Volume” setting, which is significantly slower (more than twice the render time in these examples!). It works as expected when set globally, albeit slow. It works when seen from outside the object when used locally. When seen from inside the object it does not render correctly! Afaik, it was previously possible to place the camera inside the volume, and render correct volume effects. Is this a bug??
“Inside Volume” is completely different than “On Surface”. It creates a truly volumetric texture effect rather than just simulating how far a light ray can travel and uniformly scattering it.
It’s also interesting to see the difference when applying noise. With “On Surface” the result looks… extremely poor. With “Inside Volume” it looks great. I remember it as being a lot more similar.
This is expected and there were no changes to this. “On Surface” literally applies the texture on object surface (like a flat texture). “Inside Volume” makes the texture truly 3D.
And while we’re at it: Is it possible to add a “opacity” map slot which can be used for this kind of noisy effect? It would simplify things a lot.
Can you share an example where exactly you would like to use this option? Generally, if volumetric absorption is set to pure white, it will render as fully transparent in those areas.
Also, having the possibility to make the edges of the volume material fuzzy (i.e. make the edges dissolve/fade) would improve the usefulness of the material significantly. Would love to have an option for that.
We already have this logged as a feature request.
(Internal ID=299270723)
Oh, and having the “On Surface” mode automatically clipping the bounding object to the camera (never breaking the effect from being inside the volume) would be EXTREMELY useful.
I am not sure if I understand this correctly, but I think this is exactly what we have in the V10 daily builds - https://forum.corona-renderer.com/ Chaos Corona 10 for 3ds Max - Daily Builds Changelog
Other than that, please check out this video (at this time stamp we are showing how the “on surface” vs “inside volume” modes work, but I can recommend the whole 5-part series):