My sister is an organic chemist that used to work for the company that makes the base formula in most if not all rust converters. She explained it to me that the product changes the iron oxide into a stable iron compound that is naturally dark in color and then the various additives are fillers and UV stabilizers mostly. Here is a write up from a vendor about how it works:
"What is Rust Converter? Rust Converter, a water-based primer, contains two active ingredients: Tannic acid and an organic polymer. The first ingredient, tannic acid, reacts with iron oxide (rust) and chemically converts it to iron tannate, a dark-colored stable material. Tannins are a group of water- and alcohol-soluble natural products extracted from fruits, trees and grasses. The second active ingredient, 2-Butoxyethanol, is an organic polymer that provides a protective primer layer. The overall chemical reaction converts rust into a stable, black protective polymeric coating that serves as an excellent primer for both oil and epoxy based paints."
To use properly you need to remove all rust scale and loose particles, stable surface rust is ok, then apply to stabilizer and let it dry. During the drying process the converter changes the rust. The trick is if you remove all the rust before application there is nothing to convert. I used to have problems with that part of it and had my sister watch me because I never got the color change. It was because I removed all the ruct. In that case she said just prime and paint as you would any other bare metal.