The third party overlay brings about the behavior I desire in my mouse, wish it were os integrated, but I won't complain about the color if it does the job.
As I said, I have checked the "Hide cursor while typing" box, and cursor stays on top. At first I thought it was my logitech bloatware that was making it front and visible, so I removed it, with no change.
I liked the last disclaimer of the site you pointed me to
"While this setting should be followed by all programs, it is not the case: some third-party applications, even some programs created by Microsoft (like the free WordPad editor, included with Windows), do not respect your preferences. Most should, though"
none were, not even windows os.
Thank you for your reply though.