What you've read is that with a quick "flick" of your hips you can rotate your boat back level beneath you. And it works. You're supporting yourself on your paddle shaft, and your twisting hips actually rotate your kayak back to an even keel. However, and this is key to your whole return to stability, it's not going to feel as if your hips did the work. As far as you'll be able to feel, you've just lifted the lower side of your kayak with your knee. It is just as true in a touring kayak as in a whitewater boat.
Let's try it on the beach. With both feet on the ground, rotate your right hip counterclockwise. That's a hip flick, and if you were in your kayak with the right side low you'd experience a powerful righting motion.
Now, raise your right knee and rotate your right hip counterclockwise again. It's going to feel as if you threw a lot more power in the motion. The twist or rotation of your hips is the same, but raising your knee adds to the momentum.
Get back in your kayak. Plant your foot on the foot peg, rotate your right hip counterclockwise, and at the same time push your knee up against the underside of the deck or the braces. As you do this, you'll feel your left hip and buttock push down. The result is that your boat is going to rotate. If it is canted with the left side high, you're rotating the boat right back underneath you.
Play around with the motion for a while. Lift one knee and then the other, and as you feel your hips go up and down, you'll feel and see your kayak rock.
If you lock up your knees, either by leaning back as if you were lolling in a chaise lounge or by standing on your foot pegs, you won't be able to lift a knee or rotate.
Try this out, with the help of a buddy in the water or the friendly edge of a dock. Pretend your arms are holding a paddle in a great brace, and rotate your kayak up on its side beyond the point of capsize. Do your hip flick, and the boat will come right back under you. OK, it may not the first time, and the second time may be a little ragged, but it WILL happen. And from your point of view, your lifting knee brought your boat level.
If you really got into studying your response, yeah, your powerful lower torso muscles "flicked" your hip and righted the boat. Your knee controlled the direction and force of the righting motion.