How the heck does this thing work?
Get ready for SCIENCE!
The TV knows how to generate any specific color by comparing the phase difference between the colorburst signal at the beginning of each line of video and the video signal at any point on the screen. The Apple /// generates the colorburst using one reference frequency, and generates the pixels using a slightly different reference frequency. (Why? Who knows.) This means that all of the colors are shifted “left” on the color cycle by an exact amount.
There are two ways to fix this: fix the pixel generation (hard/expensive) or fix the colorburst (easy/cheap). Phase 3 takes the colorburst reference that is injected into the 74LS11 and routes it through a series of inverters. Each hop through an inverter delays the signal a tiny bit, shifting the signal “right” and putting it back in phase with the pixel signals. It then injects the fixed signal back into its onboard 74LS11. This makes the colors match what they should look like.