While it's an amazing technical feat... is it just me or does this animation look someone's first attempt at CGI? There's some unnatural quality about it that just makes it feel wholly fake.
To answer your question. The cameras on these spacecraft is a black and white CCD with a color filter in front of it. It takes a picture, moves the filter wheel, takes a picture etc. Once the images are downloaded back to earth, the colors are added together to get a 'real' color image. The thing is that this takes time. So the first image is taken and about 30 seconds pass. In that time the spacecraft is moving, as is the moon and the earth. Then the second image is taken. The ring of green around the moon is the result of this time change. They will most likely go back with time and fix this, or the raw data will be released and a space imagery fan will do it for them. DISCOVR's earth facing camera is there just to give us a picture of the earth. There is no real 'science' done here. For those of you who follow politics, this is the camera that AL Gore wanted to put into space about 15 years ago.