my two cents....
The fact that it cleared up with the addition of chlorine leans towards it being algae. If it were metals causing the green hue, shocking would have caused it to fall out of solution and stain the pool.
I'm with the rest. TEST FIRST and report the results back to us. Also, you may want to upgrade to a K2006, that allows you to test free and combined chlorine to very high levels. In most cases with indoor pools and Salt Chlorine generators, it's easy to overchlorinate as there are little usage, tend to be smaller volumes, and little to no UV to consume the chlorine (and you have a cover too in this case).

I'd bet that the well water is very high in organic loads or some other "stuff" that is creating a chlorine demand that the salt system cannot keep up with. Again going back to the suggestions of the rest, shock the pool to overcome the chlorine demand. Check your filter for debris/algae. Test and report back to us.

Sorry, nothing new to offer from what already has been offered.