For simplicity I have only added a single point of scattering
Here we have white light that is incident an object. When it hits the object, light scatters in ALL directions. The light the enters the eye, is the ONLY light that I see. no mention of "the light ray that doesnt enter acts as another source that propagates to the eye," this is wrong.
So as of now, if I were the eye, I would register the only light I see, is a green object(or a single point of green as I have only included a single point of scattering), and the rest of my vision is black. This is similar to the sun in space. In space everything is black, apart from the point at which the sun is, as the rays from the sun move in straight lines towards my eyes.
Now what If we add walls?
For simplicity I have only added a single reflected Ray from the green object. The light that doesn't initially reach my eye, gets scattered by the wall in all directions!, the light that doesn't get scattered in my direction, I don't see, the light that does get scattered in my direction, I do see.
(Including all of the scattering elements from the wall and not just a single one) From this POV, you should technically see a green wall as green light is all that is scattered. However in the diagram I have drawn blue. This is because the white light from the torch is also scattered by the wall, which I have chosen is predominantly blue that is scattered. However in reality, it should be blue + a tint of green.
I hope this clears it up.
In general, white light enters an object, only part of that light is scattered, giving it a specific colour, the light that is scattered directly towards you , you see, and your brain registers it as a coloured object.
No extra sources required, light rays don't produce new light rays. Huygens principle is what is confusing you I'm pretty sure. This is already accounted for in the fact that you consider the net EM wave propagating and not a single element, these cancel out the apparent "source" of light from a direction not travelling straight toward you