All subscription boxes and one-time boxes ship on the 15th of every month (if the 15th is over a weekend or holiday, it will be the next business day after).
If you order goes through anytime on or before the 15th at 12PM EST, it will ship on the 15th. EXAMPLE: You place your order on August 28th, your box will ship on September 15th.
The Disney Marketplace orders will ship in 2-4 business days after your order is placed.