Steering Delay with PS4 Controller

Ive bought NFS Payback exactly a week ago and I'm really enjoying it. Something that I've noticed from the start, however, is that theres a delay between pushing the joystick to steer and the car actually steering. At first this was a slight annoyance, but as my cars became faster and faster this delay really affected the vehicle control. At this point I'm trying to get 3 stars on all the side activities but this seems almost impossible as I'm racing on the highway with a level 399 Koenigsegg and it is almost literally impossible to dodge all the traffic with this delay. I've searched all over the internet for sollutions and none of them worked. I've tried connecting the controller to my PS4 with the charging cable, tried different controllers, putting my TV in game mode and even connected my PS4 to a different TV, but the delay was always there. I really hope someone can help me solve this issue as I'm almost giving up on the game because of this delay, which I think is a shame for something I paid for and have otherwise really been enjoying.