Very common occurrence! I believe the term is "crocking". This is where the dye in pants will abrade into the top coat layer of the leather. I've had good success with Leatherique Prestine Clean to help in cleaning up this mess!
Often unknowing detailers or the owner will attempt to remove these unsightly dye transfers with chemical processes that are quite harsh for leather, or they will try abrasive means like “magic eraser” or good ole elbow grease. Some others will use heat and/or try to steam out the dye. All of these as your first attempt are much too aggressive, and in fact they are likely a means of setting the dye into the hide.
About 90% of all automotive leathers are Urethane coated, some times called top coated leather. If you are unsure a simple scratch test will help. Take your finger nail and gently gently scrape the hide. If the hide changes color then it’s likely NOT top coated. Urethane coated leathers have a slight to very “plastic” feel to them. Prestine Clean will work fine coated or not.