Hi Bud, I'm in Greenback, just outside of Knoxville!
When I had my well dug, memory tells me they let it run for a day or two to run most of the muck out of it. Later he installed a whole house filter and we've been fine ever since.
I ended up with a gusher. I don't recall the exact specifications but they drilled down to something like 200' before they finally hit water. They stopped drilling at 300' (or so I think I remember) and the water column filled up about 120' in depth so I've got a column of water 120' tall and a fill rate of over 100 gpm. They put my pump something like 10 or 20 feet from the bottom. I suppose that is to help "filter" a touch simply by pulling from higher up in the column.
On the whole house filter, he simply gave it to me and I installed it. I later asked about getting a more fancy version (read more expensive) and he shook his head saying what he gave me is more than adequate for my needs.
After 10 years, I agree.
Regarding your tinting on startup... do you have a gusher well that might simply be turbulent enough to raise some muck in the water?