Most programs will tinker with their list up to the deadline (6/4). We've started to hash out a tentative list already and will jostle it around until the deadline.
Some tips....
If you are really interested in a program you should let them know. Be specific if they are your top choice or in your top few. General interest notes aren't as powerful as saying, "You will be my top choice." Although that says something to us (more than the generalized notes/emails), understand that we won't necessarily believe it 100%. Everyone has been burned before!
If you haven't sent a note or an email and you are interested in the program you should definitely sit down and do that immediately. We take it as a sign that you aren't interested in us if you don't send a follow-up after your interview. Although we may love you, your ranking will reflect the fact that we haven't heard from you.
If you have a mentor who is willing to reach out to a program for you, ask them to do that for your top choice. They may start with an email in which they talk about how awesome you are and let the program know that it's your first choice. Then, if we have questions, we can write back or call.
Hope this helps.