I just posted elsewhere about the D-Jet cold start system and thought I would post here since it's often misunderstood. Really it's quite simple. Unlike the other injectors, the cold start system/wiring is not part of the FI system. The cold start is separate system. It doesn't connect to the brain/ECU at all.
The cold start valve (CSV) has two wires that connect to it, power and ground. That parts obvious, but where those wires go is the real trick.
The power side of the cold start valve is tapped into the starter wire. That means the CSV only gets power with the engine is cranking. Once you let that key off and the engine is just running (or stumbling) the CSV is no longer powered and no longer able to spray.
Power only while cranking.
The ground side of the CSV runs through the 'thermostatic switch'. This is the brass guy just hanging out near the engine case. It doesn't really sense anything, but reacts to temperature. The thermostatic switch is connected /grounded below 32-degrees. Anything above that and it's disconnected.
Ground only when below 32-degrees.
I've talked to a lot of people who have mentioned a 'problem caused by the CSV' and while it's always prudent to be thorough and double check everything, the CSV is almost never an issue.