I took a look at the Rain Bird ESP-Modular User Manual.
From what I can tell on the second picture:
- I do not see a Master Valve/Pump (MV), so nothing to M on Rachio
- 1-12 go directly to 1-12 on the Rachio
- All COM wires go directly to C on the Rachio
- VT is used for a “valve test” so would not be connected to Rachio
Last picture:
- The wires coming from the transformer (white, red, & green) do not go to Rachio. You will use the power supply supplied by Rachio.
- It appears that you have some sensor (red, white, & brown). I would probably suggest getting it working without this and decide later if you want to use it.