I actually sent all my evaluators an email after I entered their email address into the application to confirm if they had received the email from AADSAS. That way you don't look like you're hurrying them along, but instead are subtly reminding them to submit that letter asap. Also, don't worry- your application doesn't need to go in on June 1st. You have 2-3 weeks after the application opens before the first batch is even sent in. You'll be fine!