Tan colored spots are mostly just collection of melanin pigment, called freckles. They are normal usually in sun exposed areas. They occur commonly in summer and usually disappear by winter. Although you do not go out into sun much, they can occur without any relation to sun exposure, if you are genetically predisposed. In such case they may not disappear. But usually apart from cosmetic issues, there is nothing to worry about them health wise. You can get them removed if needed with help of laser treatment etc. But if you find any increase in size of these spots, or an abnormal change in color or texture of skin, I suggest you to visit a dermatologist for evaluation.
Another possibility for such spots is a fungal infection called Tinea Versicolor. It can sometimes occur as tan color spots over back or chest area without any other symptoms in light skinned people or as hypopigmented spots in dark skinned persons.The causative fungus malassezia is found normally on human skin, but sometimes grow in humid and warm environments causing Tinea versicolor especially in adolescents and young people. The spots can become scaly and itchy sometimes and may merge into larger spots over time. Treatment is by application of anti-fungals like selenium sulfide or ketoconazole.
Hope this helps. Do get back to me if you have any further queries. Thank you