@drewsg - a) I second @Mckynzee 's step 1 (and I’m not even a Rachio employee like she is!).
b) One would REPLACE the Intermatic with a Rachio or Rainmachine, not wire to it.
c) To get the best bang for one’s irrigation watering buck, I’d replace the indexing valve setup with individual valves. With individual valves an intelligent sprinkler controller can water only the zones that need to be watered, instead of every zone, ever time.
d) For a Rachio (no experience on the Rainmachine, but I’m assuming (we all know the breakdown of assume) it is similar) controller to work in this configuration one needs a pump start relay and a weatherproof box to put the relay into (if the pump start relay is located outside - I believe this installation is inside). Along with a weatherproof box for the controller, unless it is mounted inside.
Here is a blow by blow description of how one Rachio owner replaced their Intermatic timer and changed to individual zones:
Reader’s Digest version - replace the Intermatic with a pump start relay, which has connections to power and the pump, in a weather proof box - if installed outside, connect the pump start or master valve terminal on the intelligent sprinkler controller, also in a weatherproof box if installed outdoors, to the pump start relay input.
e) Not sure what the transformer is used for - would need to follow those wires. It shouldn’t be for the pump as the pump will be either 120 or 220 VAC. Could be for something else and just stealing 120 VAC from the Intermatic line connection.