I have no idea what this has to do with the Golden Ratio, however, if you want an exact pattern to follow, then I think it would be better to colour code and label the tiles. The pattern on the tiles makes it look more complex than it really is, so perhaps better to simplify these as just tile shapes. This is really a manual job, and there's no way to automate it as far as I know, also there are probably many variations possible for tiling these shapes.
I made this in Inkscape, however the same should be possible in Illustrator. Although Inkscape has many more snapping options than Illustrator, which makes snapping these shapes a breeze.