The red light does not stimulate the "green" cones, but the eye as a whole, being an outpost of the brainm, has a little computing power of its own. So as not to overload the brain, the light signal along the optic nerve is moderated at eye level. The most obvious manifestation of this is the iris opening and closing due to overal light intensity. Also the "gain" or light sensitivity of the retina increases slowly when in dark surroundings, and reduces swiftly when going back into the light.
The complementary colour trick is just the eye's processor trying to even out the colour blance. Look at your colour photos taken under tungsten light but with a daylight film. The picture has an orange cast, and indeed this is almost how we would see it if the eye did not average the scene to try and maintain a "White Balance".
So you look at the red card and the eye has an attempt to reduce the amount of red so as to bring about a balance and so generates a phantom green signal to try and neutralise some of the red. This effect does not switch off immediately, and when you look at the white card the green phantom signal is visible.
The same thing happens but to shapes when you look at a lit window from inside a dark room. After only a short time a negative image of the window is formed by the eye, and this becomes visible when you look away or even close the eyes.
The main thing here is that the after image, either colour or negative shapes, is not realy dependent on further stimulation but is generated by the eye as a regulator. It has nothing to do with "red" or "green" cones. Rods detect light intensity and are more sensitive; cones detect light wavelength and hence clour.
Stay safe and live long.