The language of the information we have so far is kind of vague, so we may not need actual proof of being here ON the 15th. Remember that many people who are eligible under the new policy weren't aware that they'd have to show proof.

Anyway! An email wouldn't necessarily prove you were in the U.S. since you could've sent an email from anywhere in the world. I wouldn't worry too much about it though- if you have proof of being in the US early in June (receipts, bank statements, medical records, etc) and then around or after June 15 that will probably be just fine. There have been a few threads made discussing this topic so I recommend doing a search on the Lounge section, or even just going a few pages back in the topics.