Sorry I can't answer that because but it's a bad way to think of it (IMO) I would never recommend you think Dorian, Mixolydian, Ionian for clarity, because there is no clarity.
I can't help feeling that you are trying to run before you can walk, tritone substitutes are a relatively advanced harmonic concept, and I can tell from the wrong assumptions it might be best to learn the very basics of harmony. Sorry to be blunt, but I think it's best to learn simple things before complex things.
So before worrying about tritone substitutions, learn all the chord tones and voice leading tendencies of diatonic sequences before getting onto ones that contain notes outside of the key centre.
Forget Dorian, Mixolydian, Ionian. That concept for improvising over a progression is horrible, unmusical and complicated. Especially forget Ionian, it's just a major scale. Learn the major scales, all of them. In 3rds and arpeggiated. Modes are useful when you come to play modal music, which 2 5 1s aren't.