Upon the first launch, you'll be prompted to use one of the following: Apple or Facebook account. Once you choose your method, you'll be taken to the Port as if you've just started your game. Go "back" until you get to the main menu (HQ), then go to Settings > Account (you cannot yet go "back" on an Apple device, so you'll have to play a few battles first). While there, press “Account linking” and choose either PlayStation Network or Xbox Live.
Insert your login data. You'll be prompted to choose your main account, so please choose correctly, as this is the only time you'll be able to synchronize.
Once you choose the account, you'll be asked to input the credentials once more and that will seal the deal, synchronizing your mobile and console accounts' progress, keeping it that way forevermore.
If for one reason or another you've linked your account incorrectly, contact our support team and we'll revert it, however it may take us a couple of days.
Once you've linked your accounts, you can continue playing from either your console or mobile device and use the stores on both. Once again, keep in mind that any items (specifically ships, skins, Commanders, containers, and flags) you purchase in the PlayStation Store (outside of the game) can only be used on your PlayStation console.
Go mobile, and turn the tide!