Well I'm an applicant just like you but from what I have read and understand all that we need to do is follow the terms of our offer packet which pretty much states notifying UVA about any course changes, any bad stuff we might do, and sending back our technical standards form and class reservation forms from the offer packet. Independently we should do the BLS certification thing from AHA on our own and the background check whenever it is sent to us. Of course, best course of action would be to contact admissions which I'll probably do if I don't hear anything for some time after April 30... for now I'm sure things are fine.
But yeah; after April 30 it just means that we will only be holding one acceptance to one medical school only [and then schools give out offers to their waitlist or other interviewees]. It just makes sense to me that after such point it would probably be a good time for us to receive a lot of that stuff.