The age for eligibility is given in whole years, so you are still "27 years" in June. Travelers who have not reached their 12th birthday and 28th birthday on the first day of travel are entitled to the Eurail Youth Pass. Even if you are traveling on your 28th birthday, your passport remains valid.
With a. to travel
Reduced Youth Pass, you must be 12 years old up to and including 27
at the start date of the Eurail Pass.
Terms of this Eurail Pass