Why does one part of my tour not follow my new colours?

Because that part has colours of its own. The side menu, the top nav bar, the icon bar and the pan and zoom controls each have a Use your own colours switch on their Style tab in Design, and while it is on, that part keeps its own colours whatever you set in Global aesthetics.

To make it follow again, open that part's panel, go to the Style tab and switch Use your own colours off. To keep it separate but start from your new colours, leave it on and click Match Global aesthetics: the part takes the colours, font and size Global aesthetics gives it now, and you can change them from there. Back to earlier colours puts back what it had before, such as a theme's own colours, until you leave the page.

Choosing a primary or secondary colour in Global aesthetics, or pasting a colour kit, switches every part's own colours off for you. Visitors see the change after you click Save & Render.