The deal with emails, I believe, is that if you ordered online or over the phone you should receive a shipping confirmation email. If you ordered in a store, you'd have to call the store to see if the shipping info is available (as they are the ones who placed the order, its simply being shipped to your address). The store won't know until FedEx lets them know, so don't be calling a week in advance because they'll probably not know at that point. I'd say check in 3 days before your quoted ship date.
And for those wondering, it looks as though 5/30, 31, and 6/1 orders are being processed around this time. Remember that was a holiday weekend, so don't be surprised if your order is a day late or so based on that.
My estimate for receiving your phone next week:
6/1 - Today and Monday
6/2 - Monday and Tuesday
6/3 - Tuesday and Wednesday
6/4 - Wednesday and Thursday
6/5 - Thursday and Friday
6/6 - Friday and Monday
Remember also that some people have 2 day shipping and some have overnight. I have overnight via my store order (they upgraded me for free because of the wait). That does need to be considered when matching up your order with someone who placed on the same day.