The FBI is responsible for performing the background check, and that's my understanding as to why the FBI was informed. I'm of the opinion that allegations of rape, regardless of when it occurred and if indeed that is the allegation, should be brought to the attention of those performing the background check. You're free to disagree, of course.
You are correct about the FBI and background checks. Feinstein held this until the b-check was completed—assuming those are done prior to confirmation hearings.