This is how it worked for me. I bought Black Flag as a digital download from PSN, once installed I downloaded the companion app from Apple's App Store - this is free. Once I start the companion app it prompts me for my UPlay account details and one input it logs into UPlay. It also connects to my PS4 (which is running AC4) which prompts to to confirm this connection is OK.
I wasn't prompted to purchase or buy anything. The app is free but only seems to offer functionality from within the game itself: fleet management, animus database etc.
My PSN account was already linked to UPlay although I don't remember when I did this so it must be some time back.