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Whats happening? Because molecules in ink and other mixtures have different characteristics (such as size and solubility), they travel at different speeds when pulled along a piece of paper by a solvent (in this case, water). For example, black ink contains several colours. When the water flows through a word written in black, the molecules of each one of the colours behave differently, resulting in a sort of “rainbow” effect.
Many common inks are water soluble and spread apart into the component dyes using water as a solvent. If the ink you are testing does not spread out using water, it may be “permanent” ink. In such cases, you will have to use a different solvent such as rubbing alcohol.