Yep. This isn't just a PS4/controller thing, either - on PC/mouse+kb, it's the same problem, but ONLY with Legacy controls. At least, if all of us including the OP are talking about the same problem, which I think we are.
On a mouse+kb, with "standard" movement (pressing S will make you slowly backstep), you can check an option in settings to disable all camera auto-adjustment. So this means that, even if you put your camera at whatever crazy angle you like, you can then run in ANY direction, strafe, turn, whatever, and the camera will not attempt to "auto-fix" itself. It will stay at the angle you set it at, until YOU tell it to do otherwise.
HOWEVER, with "legacy" movement (now pressing S makes you about-face and run at normal speed), even with the above option to disable all camera auto-adjust checked, when you are running, the camera will sloooowly re-orient so that, eventually, it is back to its default position behind your character. This is extremely annoying and disorienting as described above. I've always been a bit baffled as to why it's like this - there is a "disable camera auto-adjust" right there in the settings, but it seems to only work for standard controls. I've gotten used to standard, including lacking the ability to turn and run at full-tilt away from something; it once bothered me and I considered using Legacy to be able to dodge more quickly, but this camera auto-adjust while running thing was a deal-breaker for it. Fortunately with some practice, I made it a non-issue. I've gotten good enough at "right-mouse click and strafe with Q/E" for dodging that being able to use the "run straight backward" of Legacy wouldn't even give me a speed increase. However, I'm sure there are others who would appreciate being able to play in Legacy without the camera auto-adjust. And as I said, since it's right there in the settings, it's weird that it just mysteriously doesn't apply to Legacy for no discernible reason.
So maybe we can get this on the devs' radar? Would be a small change, but a welcome one.