While you are not looking at the Green and Purple areas for long, my guess is that you are looking there or you wouldn't be able to make the corner flow.
If you feel that your line through a corner is pretty smooth and fluid, then my guess is that you are seeing those points and your brain is making the bike connect the dots with a smooth turn. If however, you find yourself adjusting your lean angle erratically while navigating a corner, then you are not picking up the points and judging your speed and cornering line appropriately. The movement or leaning of the bike from turn-in to apex to exit should be a steady "one piece" motion Gradually leaning in to the maximum lean angle needed to complete the turn for the given speed and line and then gradually leaning the bike back up to being straight up and down. If you are constantly readjusting your lean angle then you don't have all of the pieces of the puzzle put together correctly.
This could caused be any number of reasons: Incorrect reference points that result in the wrong line, incorrect speed for the lean angle you are attempting to carry, different entry speed, etc.
Where you looks is very important in terms of setting the reference points that your brain will use as you negotiate the corner, but that is only one aspect of being smooth. You really just bounce your eyes off these points as you navigate a turn and then use your peripheral vision to work your way through the area based on the reference point your brain picks up when you glance at it (even for a split second).
Once you get to a track day, talk to a control rider and ask them to take you out and show you the proper lines for the track. As your speed increases, these reference points will change, so it is more important that you understand how all of the pieces of effective cornering work together so that you can make adjustments as you progress in your riding skill.
I know that I don't use the same points in "A" group that I did in "B" group, particularly where Braking Point and Turn-In point are concerned. The Apex, while a clearly defined point in a turn, will change depending on traffic and how you are negotiating it in a turn (if you are). Different lines offer different benefits, but you must first learn the ideal line, get used to it, be able to repeat it. Then, you will be able to experiment as you progress.
Most track day organizations do not allow passing in the turns in their beginning group so that you can concentrate on learning the ideal line without fear of someone taking it away from you before you are comfortable riding that close to someone else and having to modify your line at speed. Then they move you to passing only on the outside in the Intermediate group and ask you to allow 6 feet of space between you and the person you are passing. Finally, when you make it to the "A" group, you are free to pass anywhere on the track, but block passing and stuffing are highly discouraged and frowned upon in the track day world. But, I can tell you that I have rubbed elbows with many people in the "A" group at speed in corners. It takes a while to get comfortable with that, but once you have ridden that way, any attempt at riding fast on the street suddenly has no thrill to it...
Sorry for the long and rambling post, but there really is no quick and simple answer to your question. Time on the track and working with control riders will help all of this make sense over time...
Jeff