I think the car will swing around to the direction you were pointing when you pressed the button.
Quite a few times I've pressed the button THEN looked the direction I want it to point and it looks the wrong way.
Hmm. I can't confirm or deny this at the moment
I feel like there were times where i was standing still and i'll call the batmobile and the camera will automatically focus on wherever the batmobile is coming from and then it'll still swing itself and point me in the wrong direction
EDIT: Here's a clip from a stream i was doing yesterday. I'm up on the rail, i see a car i want to chase, i drop down facing the direction the car is moving and you can see the batmobile symbol appear as i'm headed to the ground and the batmobile comes and completely points me in the opposite direction and then i go to find the car but i lost it. Between waiting for the animation for the batmobile to show up and it potentially pointing me in the wrong direction, i lose out on small things like this in the moment. Again, not a huge deal, just a bit of an annoyance.