As ex-Benneton F1 mechanic and SPEED "Technical Color Commentator" Steve Matchett has explained it, the switch is located in the nozzle of the fuel rig. Since he knows most everyone in the garage, I have to assume he's talking from a position of direct knowledge.
When it disconnects from the car's receptacle, it signals the light to go green. I would not be surprised if it did this even should the nozzle still be right next to the car. Since it takes a second or so for the driver to engage the clutch and launch the car, that gives the fuel guy has enough time to pull the nozzle back and away and allow a clear departure.
Since fuel delivery almost always takes more time then tires, I can't see the tire guys having their own switch. Especially since they all still put up their arm, which is the signal to the lead mechanic that they have completed their work. It would also be four more possible points of failure or personnel miscue to cause a longer stop, which this whole light thing is meant to prevent.
What most likely happened at Singapore was the fuel guy started to pull the nozzle, but it jammed. Yet for the moment it was "off" the car's receptacle, that was enough to trigger the green light.
The Head Mechanic can override the lights, and it looks like he either did that or the fuel guy reconnected the hose to try again, since almost as soon as the green light went on, it went off and the red (or amber?) light came back on. But by then, Massa was already launched and could not see it change.