I just did an experiment.

First, I took two pieces of construction paper, orange and green, and held them between my light source and a white sheet of paper. (I had to put a piece of cardboard behind the construction paper to prevent the light from shining through the paper.) The shadow cast by the paper was neutral, with no evidence of the green or the orange reflecting onto the white paper.

Second, I moved the construction paper so that it faced the light and then put the cardboard between my light and the white paper. The shadow cast by the cardboard contained lots of green and orange light cast from the colored paper.

Here is a crude diagram of what I did. The top diagram, with the colored paper in the middle, cast a neutral shadow. The bottom diagram, with the colored paper reflecting back, had a colorful shadow.

reflected light diagram