Played about an hour and a half of training missions and a tiny bit of solo last night immediately after the launch. My PS4 had already downloaded and installed the initial patch before midnight.
I'm on a regular PS4 and definitely see screen-tearing. So far only really noticed it badly when using head-look, and it's by far most noticeable inside stations. I messed around with some of the head-look settings, softening, etc, and thought I got it looking a bit less obtrusive, but that may have just been my wishful perception!
It also appears when using the camera suite. I was having a look around my ship in the hangar and moving the camera around caused really obtrusive multiple tears across the whole screen.