Yep those are just bright spots of light reflecting. Due to their brightness compared to things around them they are bringing out the chromatic aberration in the lens. Nothing you can do about this. Some lenses just exhibit this problem when used in extreme fashions or used in ways outside their intent.
In this case it's a bit of both. The 105mm macro shot here is at f/2.8 with a long focus (the worst possible situation for a lens designed to be used stopped down and at its nearest focus point).
I think you'll find if you raise the aperture to f/5.6 it'll all go away. Those other big gobs of spots on the original images will likely go away if you use a lens hood. Your 50mm f/1.8 will exhibit the same problems at f/1.8 but you may find that at f/2.8 it's fine.
A good place to have a play is at a river or some lake. The reflection of water is always a great source of purple fringing.
I do the same thing with my 50mm f/1.2. It's a horrid lens that I never use at f/1.2, but it's sharper than my 50mm f/1.8 @ f/2 so I never use the 50mm f/1.8 anymore.
If you really must shoot wide open (portraits) and the CA is worrying you it's actually very easy to make it disappear in photoshop. Heck even some raw converters have a "de-fringe" option which works with varying degrees of success.
The method I use is this one here:
Photoshop How-to Remove Purple Fringing
Basically it involves de-saturating exactly the shade of colour that the fringing causes. If you have other cases of blue and purple in the image then layer mask the hue saturation adjustment layer so it's only affecting the purple fringing.
By the way how are you post processing these images? Do you shoot RAW? And if so do you use the Camera profiles options in Adobe CameraRAW / Lightroom? I ask because it looks like you've clobbered your black values on that shell. It's not very smooth, there's lots of surrounding detail and then black.