Aerospace engineer here: Producing lift in either the up (airplane) or down (spoiler) direction generates induced drag. The amount depends on your design, in that a large real or effective AR can reduce it, but it's going to be there.
I think what happens in automotive designs, which are not always penned with the same attention to aerodynamics as aerospace designs, is that they often have unintentional lift at the rear. Adding a small spoiler, then, doesn't add actual downforce, it just reduces lift -- and therefore reduces drag into the bargain.