As Lord Lew said, you have to actually add the code for the High Seas booster to your account via the Account Mangement system.
The code will show up at the very end of the ordering process on the Origin store and also in the order confirmation e-mail message that you receive from Origin. (The e-mail subject will say something like, "Origin - Order confirmation for order #123456789012.")
Log into the Account Management system. Then select the account you want to apply the High Seas booster to from the drop down box at the top center of the page. Then click on the orange "Activate Key" tab. Enter the code from the e-mail in the top box and then enter the captcha code in the bottom box and press the "Continue" button.
If you entered the codes properly, the next screen will tell you that the upgrade was applied to the account. You can also double check it by clicking on the orange "Subscriptions" tab and then scrolling toward the bottom to see the details of the account you're currently viewing. Click on the "Features" tab and then scroll through the list until you come to the one that says "High Seas" and confirm that it says "High Seas enabled" underneath it.