I don't think SEGA genuinely believes they are going to capture a new audience on Xbox. They are definitely not stupid, they have decades of data to pull from, including prior releases they've made this gen.
SEGA takes the PS audience for granted is more the thing. There is very little need for them to market on PlayStation. Persona has a very dedicated audience already, and given that it's a relatively niche genre, it's not an audience you need to sell to -- they generally already know whether they want to buy it or not.
To them, marketing excessively to an audience that is either already convinced they'll buy your game, or already convinced they don't care, is not worth as much as the bag of gold Microsoft is throwing at them. SEGA also doesn't give a fuck about Persona, ATLUS, or anyone else. They care about them less than INDEX Corporation did.