Kasumi already felt loved by Aki, she just didn't know that Aki loved her this way. Unlike the "I love you's" she has been manipulated with so far, a tearful confession from the girl who has been there for her during tough times is more than just empty validation.
Kasumi also dropped an "I love you" to Aki while she was staying at her place. Platonic as it may have been at the time, it was definitely affectionate.