Yes, they have made memories together for the last four years but if it wasn't enough for her to not end the relationship, what makes you think it would be enough for her to not find someone else? If there's one thing I've learned in the last couple of months, it's that anything can happen. Memories, feelings, and promises mean nothing. They can dissipate in the blink of an eye and leave one person absolutely dumbfounded.
Just because she agreed to date you doesn't mean she's dating you exclusively. The problem that you have now, however, is that if you start asking about this guy, you could likely get an answer you don't want or you could start to push her away.
I don't chase, I replace.