Ah, I don't know if 'activating the core' is the only problem here. The first rep isn't
too awful, but the rest of the set is, sorry to say it, horrible. It looks like you're reaching for depth with your shoulders - not good-morning the weight up but good-morning the weight
down. Very strange indeed. It'd be a good idea to watch
this video on back control during the squat. It might also help to practice going into a full-depth squat with an empty bar or even a broom-stick and getting a video so that you know what it feels like to go below parallel with your hips (not your shoulders!). I think that a deload alone is not enough to fix these issues - you really need to go back and learn the movement all over again, because this is going to fuck up your back really quickly.
Sorry if that's a bit strong, but I wish someone had told me the same thing when I started - would have saved a few pulled muscles!