I don't think your problem is that "Mathematica didn't do it right". I see Mathematica DID insert glowing green when I look close.
Overlayed image is a nice but old trick but does not look like it was the problem.
Your problem seems to be you "luckily" got a color effect in blender - which didn't even render the image "right". In mathematica (the code for neither did you show), you did not pick COLORS (ex: a very bright colored yellow inside a light blue translucent would provide a bright green) - but you comlain in mm it's hard to see but you used a darker blue to cover it. Furthermore the blender image appears to be CULLED (the face taken off)
It even appears as if the blender model was specially made in blender to cut off the face (the darker blue face) to make the 2nd inner "very light blue" color the only visible surface between the ball and camera: which you didn't do in Mathematica, but could have.
But Mathematica clearly has that ability, to cull shapes using planes or even other shapes or even textures.
But you also didn't show code fore either Mathematica or Blender.
the blender image has a serious issue: neither end of the tube shows any "3d clues" for the outer darker blue cylinder, the darker blue shows only 2D clues. it's either a composite image or mistakenly rendered. only the lighter blue tube shows "3d visual clues"
I think Blender does ray tracing as well as "openGL" live graphics. 3D/GL won't any time soon look as good. Mathematica has only a minimal renderer that is not "mouse driven" (3rd part at that). blender likely has a great mouse interface mm is missing, that's very likely true - but blender hasn't any math or or sound engineering, so.