The validity of the sim card starts immediately after receiving the confirmation of activation.
If you have a 30 days plan and if you submit the activation of the sim card on June 1st it will be valid until June 29th (23h59 GMT-5 – New-York time).
Note that if you schedule the activation with a departure date for June 2nd, your sim card will be activated on June 1st and valid until June 29th (23h59 GMT-5 – New-York time).
The first day of activation count as 1 day.