My interpretation is that in the first video you posted, you're dropping your hips too much in the set-up, before you lift the bar off the floor. Keep your hips high while you set up, let the "chest up" movement squeeze some upward force against the bar, and then concentrate on pulling the floor away from you with your posterior chain. The rest will take care of itself.
Step 1. Grip the bar.
Step 2. Bend the knees so shins touch the bar (DON'T DROP YOUR ASS)
Step 3. Chest up, squeeze the bar, pull.