Colour perception is achieved by three types of cells in the retina of the eye called cones.
With the three types of cones, one is more sensitive to red light, one is more sensitive to blue light and the other is more sensitive to green light. Each cone reacts at different speeds to light and keep responding for different lengths of time. You only see white when all three cones respond equally.
What you are seeing is an 'afterimage'.
When you stare at the red parrot the image is perceived by only one area of your retina. Eventually this area of your retina gets tired and stop responding strongly to red light.
The white card reflects red, green, blue and every other colour of light.
When you quickly look at the white card after staring at the red parrot, your tired eyes do not respond to the red light being reflected. This allows the afterimage within the picture frame to look bluish-green or 'cyan'. The same works with the other colour parrots;
Stare at the blue parrot = yellow parrot in the picture frame (red light + green light = yellow light)
Stare at the green parrot = magenta parrot in the picture frame (red light + blue light = magenta light)
