Why is it that gems/ rocks, such as Ruby, Sapphire, Topaz, etc... all have their own unique colors? Is this something that happens from chemical attraction with each stone upon formation?
There is no simple answer to this. The colour can be caused by trace or minor elements in the gemstone. Cr, Ti, Mn, Fe, Co, Cu and a few other metals have a strong colour control, as does their oxidation state. eg. Chrome and titaniaum gives the colour of ruby, iron gives the colour of olivine. Another effect is disruption of the crystal lattice, e.g. by heat, internal radiation, artificial radiation or physical shock. Then there is the intrinsic molecular structure of the mineral itself, as in moonstone. Schiller effect, and similar arrays of colour can be caused by optical interference between micocrystalline twins or microscopic intergrowths of two similar minerals, as in various varieties of feldspar. Other effects are pleochroism (Alexandrite), trichroism (Tanzanite), Chattoyance (Tourmaline), and microscopic inclusions (various forms of silica).
It is quite a big subject, but there are many good well-illustrated texts to read more.