So after you've purchased your PCG points to your account and you've purchased Mystery Boxes through the web based shop, how do you claim them?!
First, you should be on the Myster Box section of the website, then you click on View My Purchase History, as shown below!
The on that screen, you have the option to send individual items to in-game or you can select Send Top 25 Items, as shown below.
Then you can access them in game!