This needs to be explained with shadow masks, but life is short. A shadow mask preserves the gemetric realtionaship between the position of the three RGB electron guns and the corresponding phosphor dots. Needs a picture, really.
Yes there are fixed phosphors on the screen, arranged in vertical R, G & B stripes or bars. These are clearly seen on a TV, but not so obvious on a monitor where they are closer together. From the scanning electron beams point of view, these are effectively homogenous, so it doesn't exactly matter where on the screen the beams land, they will always hit a phosphor of the right colour.
Think about it, what would happen if that wasn't the case? The beams cannot register exactly with every phosphor because CRT geometry is never perfect. The picture can move up and down, left and right, in tiny movements without any terrible interference or aliasing patterns that you would otherwise get.
The really good bit is where you use three monochrome CRT tubes to generate a colour image, with CRT projectors. They do not need shadow masks, or lines, or pixels, AT ALL. If it's properly set up, nomatter how close you look, you will never see any granularity of any sort, no separate RGB colours as pixels or rainbows. A dinosaur, maybe, but flat panels are not quite a replacement.
Sorry, got to take the kids swimming, Bye, Nick