The "change in her heart" part could mean a lot of things. It doesn't necessarily means she falls in love with him.

For all we know, maybe things aren't doing too well for the resistance by the time the game starts, and maybe Ashe is starting to lose hope to see her kingdom freed from the Arcadia Empire; meeting Vaan, who seems to believe a lot in his dream, could bring hope back in her heart.

Mind you, it's just my theory, which is most likely to be proven wrong as the game is finally released. I guess we'll just have to wait and see for ourselves.