Playing while downloading game in the PS4

So, I was downloading Infamous: First Light on the PS4 and the total size it says "9.6gb" to my surprise at 6 and something I could start the game, but some "data app" has started downloading. My question is, is there a problem if I start the game like that? will I have performances troubles and stuff? I´ve been reading and this looks normal in some games, like The Last of us but I´m not sure if is more like "to test" the game or to play as normal.