Video: YouTube
Video: YouTube
You appear to be laying back by extending the hips, not by hyperextending the back. You are doing the Press correctly.
The only thing I’d say is you may be able to speed up the transition from the layback to pressing. There’s a bit of a pause there.
I'd agree with above.. you look like you're extending at the hips rather than the spine. As long as this is the case and you're bracing your core to keep your spine neutral, you should be fine in that respect.
I'd also agree that you're not getting any rebound out of your lay back and instead just pressing from a pseudo incline position. If you can use some of the rebound to press the bar up it'll make for an easier lift.
It's about as common to hear people say that as it is to hear them say "squatting at or below parallel is bad for your knees." The thing you need to watch out for is hyperextending your low back and even if you do that, you probably won't experience much pain. If it does happen, though, just focus on contracting your abs harder.