This complex process is much easier to see in an actual schematic, we'll follow a CTC-2 here because it and it's sibling the CTC-2B were the only original chassis to faithfully follow the NTSC standard to the letter. All following chassis made some variation on how they went about both recovering the signal, and at what phase angle the signals were demodulated (hence other terms besides I and Q being used to describe the chroma signals such as X and Z).
The full schematic can be found on the ETF site here:
http://earlytelevision.org/pdf/CT-100SamsSchematic.pdf
In this first shot, we see the fist video amplifier. Brightness information is amplified and passed on to the second stage, chroma signals are filtered out at the cathode and passed to the chroma amplifier.