I have an '05 Toyota Rav4 with daylight running lights similar to yours. My D3, which I installed myself, properly dims the display.
All the wires I soldered from my Toyota harness to my D3 harness were similarly colored (red to red, yellow to yellow, etc) and the D3 illumination wire is orange/white, would have been connected to the orange wire on the Toyota harness.
I bet if you pulled your D3 and checked the wires, your orange/white wire is connected to a differently colored wire.
Here are pics of my install, if that helps any: http://rav4world.com/forums/viewtopic.php?t=12147&a