Quests don't effect the level cap. It goes uo to 60 automatically once Heavensward is installed. Something else is going on here, but I play on PC, so I really couldn't say what rhe the issues are on a PS4 account.
It's more along the lines of: Once HW is registered to your account. I have HW installed on my PS3, PS4 and PC and my account without HW registered is stuck at 50.