It's a good question, and I'm not sure of the answer.

Rust is a corrosive process, but corrosion can be limited by depriving the environment of oxygen. And if frame saver forms a sufficient coating over the insides of the frame's tubing, then it will limit further spread of rust.

It's also important to make sure the inside of the frame is dry and has had chance to dry out before applying the frame saver.

I would argue that linseed oil is very much a second (or third) best solution; it doesn't spread out and stick as well and needs to be re-applied. It's better than nothing, but frame saver is a much better alternative.

There are some products that chemically react with existing rust to prevent further spread of rust. I've seen these in liquid (brush-on) form and in aerosol cans. Not sure either one works well for application into the inside of frame's tubing.

well biked, I'm interested in the product that you've been using. What's the name?