The Aquafresh link shows toothpaste being put into a real tube-shaped tube. With no separation or mixing device. This would work because as you push the plunger from the bottom, all that happens is that the paste & stripes are compressed to a smaller diameter 'stream'. IE they come out exactly as pre-loaded into the tube, but smaller. If you think about it, why would they mix? Shaking would do not good (the mix is too stiff), the plunger has no rotational movement and you can't squish the paste from the side or middle.
Whereas the collapsible, old fashioned tubes will (I think) need the colours physically separating, as there would be no way of knowing how the user would squeeze the tube. This is as shown on the Wikipedia link.
Which sort of tube was it you cut up cazzbazz?