The activation is automatic only when you purchase from the integrated process in FSX, if you purchase on the web page, you have to register the scenery yourself, how else FSX can be notified you purchase something with your browser ?
To register your Serial Number, use the "Register Serial" function of the Addon Manager inside FSX for FSDT KLAX, using the Serial Number as indicated on the purchase receipt you received by email.
All of this is explained on the installation guide, named fsdt_install_guide.pdf, to be found under the FSX\fsdreamteam folder after installing the scenery, starting from Page 12.