It’s interesting you say that, because we haven’t really seen Roose negotiating with Tywin yet. I’ll get into this more later, but I think Roose was thinking very pragmatically about de facto vs. de jure power: i.e, once he gets back to the North with an army of 6,000 men, and kicks out the Ironborn invaders, he is the real power in the North.
Yes, on paper Tyrion is the new Lord of Winterfell, but no Northman is ever going to bend the knee to a Lannister, the Lannisters are too badly weakened to send Tyrion with enough troops to make royal decrees take, and it’s a long way from Winterfell to King’s Landing and Roose will be the one holding Moat Cailin. So if push comes to shove, Roose isn’t going to lose any support in the North if he betrays the Lannisters and “rescues” Sansa.