You can't download anything yet because there is nothing to download. Patch 4.0 is stormblood . SE has to add it in to the base game . What we have are keys to unlock that content. PSN won't download anything other than the skin/box art icon in games list. The real download comes from opening the game client and doing so when prompted to.

If you read this information
http://na.finalfantasyxiv.com/lodest...c5dcc63c#aa3_4

You can get a understanding how it works. But it does require reading it and not skimming it.