In order to unlock the unqique rewards for signing up your Starbreeze Account, you need to link your Steam account to your Starbreeze Account. If you have yet to register, go here: https://nebula.starbreeze.com/register
If you did not register using Steam when signing up, go through the following steps: My Profile > Linked Accounts > Link an Account.
From there, you can link your Steam account to your Starbreeze Account. When you have linked your accounts, you should be able to see the unique items in your PAYDAY 2 inventory
Make sure you are using the same account as the linked Nebula account when playing the game
Some items could still be unlocked if the player does not have enough reputation level or in-game money/cash