Most of the tire shine products available have petroleum distillates, not too different from the stoddard solvent in WD-40. Carrier solvent with a light oil (or silicone product for tire shine).
The tires on my 67 that I replaced last year were 15 years old, they got tire shine treatment more frequently than they got driven on. The outside sidewalls were great, the inside sidewalls were dry-rotted. That's my experience with long term tire degradation and tire dressings, they prevented it.