Hey Alton,
I don't know what MR says, but Taj Burrow in his book writes that the foundation of good surfing is "flow" involving all four limbs. So for a toeside gybe (similar but not identical to a toeside bottom turn), these steps will improve flow.
-Back foot on the traction, best of all if the back foot is on the wedge, with your back leg making about a 45degree angle with the board. This helps with cranking the turn, and also allows you to have a wide stance without the poo man look
-Front foot near the sweet spot of the board
-send the kite before initiating the turn to ensure you are powered through the gybe
-Use your head/shoulders to initiate the turn by looking at the kite as it floats to the other side of the window, along with light toe pressure. You actually don't even have to think about toe pressure if you are looking at where you want to go
-As soon as you send your kite, drop your back hand and let it swing naturally in the arc that you want to turn. For a tighter turn, swing your back hand more aggressively. This arm movement will get your fins and rail to engage into the turn. You can drag that hand in the water if you are off balance
I have never heard anyone say that good surf turns require swinging of the hips, although hip swings will occur naturally as a consequence of head/arm movements (and a big top turn will involve swinging your entire body, head, shoulders, arms, core, hips, and kicking out your back foot as you hit the lip). More often I have heard good surfers say "spot where you want to go, and the turn will follow" and "use your arms not your feet to initiate the turn".
I would watch a few videos of Andy Irons if you want to see good surf style.
https://vimeo.com/110548813In terms of translating it to kiting this video is a good one. Not super technical but nice gybes and tacks
https://vimeo.com/65205613