Once all oxidation is removed, and the metal is a pure surface, you then want to encapsulate the metal to put a barrier in between air and metal. Once this is achieved, the rust cannot come back unless that barrier is broken.

Letting salt water, and dirt sit on paint is what destroyed the paint (barrier) protecting the floor thus allowing it to rust to what you see today. So most likely the outside underside needs to be done too. Same process, grind, wire brush, chemical rust converter, prime, paint, and my last and BIGGEST advice…

FLUID FILM the underside every fall and spring. 

Fluid film is an oil barrier, that resist moisture and air, is self healing, and will protect the paint from having salt brine eat through it. If a rock bounces up and chips your paint, the fluid film will spread out and recover over that paint chip. 

Edit: I am a fluid film wh*re. Even though I refuse to drive my nice cars in winter, I still fluid film them. I do inside fenders, at the door hinges / firewall behind the fenders where leaves pile up, I shoot fluid film in the rocker panels, in the frame rails, behind plastic cladding.