When rudders are deflected, not all water flows across the blade; some "spills" over the bottom. This reduces the effectiveness of the rudder and creates additional drag, specifically called a tip vortex. A winglet's function is to keep more flow over the rudder, increasing its effectiveness and reducing any tip vortices. In order to so this, the winglet is positioned at or near the bottom of the rudder where it can act sort of act as a fence. Many airplanes have similar devices on their wing tips, though they look different.
Of course, when the boat is going straight (or no lateral forces like a sail), there is no need for a winglet -- it just adds extra drag. In other words, if the rudder is doing the job well, there is no benefit to having the winglet. But if your rudder needs more bite, a winglet can make it more efficient without increasing the rudder size.
For the Oasis, this winglet's job will be to help keep the boat from broaching on high boat wake angles. For the AI, it will be to add low speed rudder authority where weather helm is an issue (not referring to rudder balance), and as insurance against high speed rudder pop-up.
As to size and shape, I am no expert by any means. There are, no doubt more efficient shapes, but there are some practical matters to be considered:
1. You don't want your winglet to extend forward past the rudder lest it might snag seaweed or other debris.
2. You want it as small as practicable to minimize drag but not effectiveness.
3. It should be joined on both sides so strength and alignment can be achieved relatively simply.
4. (AI only) the winglet also seems to help keep the rudder down at high speeds, so the longer back tab should help. This would be a waste on other rudders though where kick-up is not an issue (except that it helps prevent it from splitting while you're building it).
Theoretically, I think it should be wider near the front (where the rudder is widest), tapering aft. I don't have the skill to make it that way, so it looks more boat shaped instead. It seems to work well enough though!
I'll add a picture when done.