You are right the mineral spirits have a much longer effect than Acetone.I liberally soak engine parts sometimes with the spiritual stuff, then let it dry and go on with regular cleaners. Seems to make the imbeded oily crud in porous aluminiums come off much easier that way.
Having said that and if the spirits got on your tire, they may make it greasy for a while. Acetone will get rid of that. But watch out with Acetone around some plastics.