Dude, she was literally told that he might be the cause of her death. Any real person would probably jump town altogether, Umi is being rather altruistic here. I don't think her hesitation based on, y'know, a life and death situation can be criticized.
if you put it that way then the MC also shouldn't tell her that she only have 100 days (with some unknown variables) left and they shouldn't bother with those things in the first place