To extend a little on what others have said, if you were to drive a boat with thrust directly along the centreline, with no yaw induced in the thrust, and edge it over, it will turn away from the low edge. My own conclusion is that this is true no matter what the length of the kayak is, or how much rocker it has.
But canoes and kayaks are not driven by a centreline thrust, they are driven by a thrust some distance away from the centreline with induces yaw away from the paddle stroke, and this complicates things, a lot.
With a short highly rockered kayak, the boat will generally continue to turn away from the direction of the last paddle stroke, whether that stroke was a power stroke, or a sweep stroke, and irrespective of which way you edge the boat over. It is normal therefore to edge down to the inside of the turn for stability, it literally feels a bit like riding a bike, it is very intuitive and everyone can pick it up almost instantly. When normally coached, this is often done with a low brace either ready above the water, or dragging on the surface to slow that side of the boat and tighten the turn.
The longer and less rockered a boat is, the less it turns away from a paddle stroke, you will almost certainly need a sweep stroke to make any noticeable yaw and initiate a turn. If you get a decent sweep in, and then drop the inside edge your boat will probably continue to turn to the inside. By edging you have increased the rocker - made the centre deeper and lifted the ends slightly, thus allowing it to turn more easily in the direction you already initiated. But if you sweep is not strong enough, when you edge the natural tendancy to turn away from the low edge might be stronger. It mostly depends on making sure the bow is already turning before edging so the flow around the kayak is already not parallel to the centreline.
On the other hand, if you drop the edge before you make your sweep, the hull may already be turning towards that last paddle stroke, and it can be a bit of a lottery which wins.
To complicate it more, if you drag the low brace on the surface, it slows that side of the boat and creates yaw moment towards the brace side, but again how effective that is depends on what you did before and how quickly the boat was already turning, and in which direction.
So there could be a lot of things going on, I would suggest it is most likely to be a difference in timing your sequence, when the boat turns towards the low edge, you will probably find you swept with the boat flat, and then edged, and when it turns the opposite way, you probably edged first and then swept.
So, I would recommend some flat water exercises to get a feel for your boat and its natural turn rate with edge. Find somewhere with plenty of space and get the boat up to comfortable cruising speed with power strokes, and then roll onto one edge whilst still paddling forwards as normally as you can, watch the bow turn a few degrees and then roll onto the other edge and watch it turn back. Keep practicing edgeing from side to side until you get the hang of how quickly it turns with different amount of edge, and also how much opposite edge you need to apply, and for how long, to stop a turn and get the boat moving parallel to the original course (wide river or canal is more useful than completely open water for judging this).
You can also get up to speed, ease off the paddling and make sure the boat is gliding in a straight line, and then edge it and see which way it turns - can you turn it back on the opposite edge before you lose too much speed for edging to cause a turn?
Also useful is to get up to speed, keep the boat flat and try turning using sweep strokes only (do several on one side).
You should end up finding out that when moving slowly the boat turns better with sweeps, and at speed better with edging. To reinforce this try getting up to speed, edging the boat to trun away from the low edge, and then do power strokes on the inside of the turn only - does it turn faster than just edging alone? Hopefully it will, and you will have found out how speed affects the amount of edge and rate of turn.
Then of course try the more obvious thing of sweeping on the low side, you probably won't notice a huge difference between the turn rates based on which side you paddle as long as you are keeping the speed up on edge - personally although I know this I do usually end up sweeping on the outside in preferecne to paddling both sides (my daily training paddle requires a 180 degree turn in the river, if I don't use the full width edge hard and keep paddling I could ram the bank - alternatively I could slow down and use reverse strokes on the inside but not ideal on a time trial).
By the time you have done all these exercises over and over again you will probably be wondering what the hell you even need a low brace turn for - well Pathbrae and Aled have covered that - when you are riding a wave, or crossing/entering/leaving a current edging to the outside of the turn will make the boat want to turn over, so you also need to be able to initiate a turn from a sweep and edge/lean into that turn, using a low brace (either ready or planted) to provide support is a great way to do that. You also have a speed differential from the current or wave which cases the boat to turn in these situations. To understand the current element, Kelvin Horner has been putting together some ace videos in the blog part of his sweet skills website about varying boat angle and speed to achieve desired outcomes - mostly filmed in OC1, but all relevant to kayaks too. http://www.sweet-skills.com/blog
tidal streams and eddies are usually on a different scale, but the principles all apply.
So hopefully after some edging exercises you will have a better feel for how your boat turns and will find it easier to time your low brace turn phases to get predictable outcomes, so for example you could demonstrate it on flat water when doing a star assessment (or whatever the new thing is).
As an aside, there are play boaters and slalom boaters who will use outside edge in current deliberately to sink the stern to initiate play moves or make a really quick turn - these techniques don't work in a high volume boat like a sea kayak, you will either capisize or give yourself a hernia!
As a second aside, in a narrow canoe where the seat position is fixed (OC1 or most decked C1s) we can make straight forward progress paddling on one side only by lowering the opposite edge to keep the boat turning naturally towards the paddle thus countering the turning effect from the paddle (which also has a small corrective flick). In wide canoes it would be impossible to reach the water doing that so the technique tends to be to edge towards the paddle and use a correction phase to straighten out the turn each stroke.