Mike
We are on the same page. That is why the program and its tutorials together concentrate on the practicalities and are light on theory, and why they demonstrate how to arrive at the main chords and chords patterns and progressions for any key without having to know any music theory beyond what a chord is. Hopefully, in time, it would all become instinctive.
My own experience is that, after finishing my brief piano lessons at the age of 8, and before I moved on to home organs and then arrangers, for 25 years I played piano at home in my own way in a hybrid fashion, a mixture of playing by ear, playing by copying and playing by reading music. Although my early piano lessions taught me to read music (as long as it isn't too difficult), I tended not to stick to it and ended up improvising the left hand part around what was written. During this time, the type of chord patterns and progressions you talked about did become instinctive. When I listen to a song, I can sketch a visualisation of the chord progression in my head from how it sounds - it may not always be 100% at the beginning but it will be close.
I also developed a habit of playing chord inversions instinctively to transition between chords, and I use chord inversions alot. I was not aware of it at the time, but I now understand that it is a technique known as 'Voice Leading'.