As you probably know, paint is used to protect metal from rusting. The reason why metal fences, unpainted car panels, and knicks in your car's paint rust is because that layer of protection is gone and the bare metal, exposed to moisture, oxidizes and turns to rust.
Keep in mind that metal can still rust even if there is paint on a surface, such as your case but moisture has gotten below the surface (or in through the exhaust itself) and rusted the metal.
Best course of action for you, is to remove the exhaust and sand the paint and rust off. It can be time consuming and tedious but once you have a smooth, all metal surface use some high temperature spray paint and it'll look nearly brand new.
I should mention from the looks of it, your exhaust just has surface rust. This can be taken off just with sanding. If your exhaust was rusted all the way through then you'd need to either weld in new bits of metal or buy a new exhaust.