Leave the paper in the water until the colors go all the way to the top edge. Try it again with another black marker and see if you make different colors. Using your black marker draw a black spot in the center. Put the filter circle on a saucer, and add a few drops of water on the spot. Let it sit for a few minutes and you'll see rings of color that go out from the center of the circle to the edges.
Most nonpermanent markers use ink that are made of colored pigments and water.
The water in the ink carries the pigment onto the paper. When the ink dries, the pigment remains on the paper. When you dip the paper in water, the dried pigments dissolve. As the water travels up the paper, it carries the pigments along with it. The speed depends on the size of the pigment molecule and on how strongly the pigment is attracted to the paper.