Hmm.... I'm not sure if this really deserves to be an answer, because I haven't done this specifically, but one thing that comes to mind is an Apple crumb cake I made from this recipe right here. Yes it says strawberry, but apples are if anything better.
The point is I think there is at least one thing you could try that might help without changing your exact recipe.
You could change the way you cut your apples, or at least part of them. If you slice the apples very thinly, you can layer them together to form a kind of platform, which can help to prevent uneven sinking/mixture. You could either stick to that method, which can lead to a very pretty, layered pinwheel presentation if there's no other topping, OR once you've got a decent layer of sliced apple to provide this platform, you could put the rest of the apples, in chunks, on top if you want that look to it. If you use the sliced apples, you will get a different texture though.
Beyond that, you'll have to modify your recipe. As a commenter stated, you need to consider things like density and surface tension. My suggestion above is a way of playing with surface tension--Less weight distributed across a broader surface means less sinking, but if your cheesecake batter is as liquid as my usual recipe is, it might not work regardless. If you switch to a simpler, denser recipe (possibly just by leaving out some or all of the cream), you should have no trouble regardless of how you cut/place your apples.
In the recipe I link, the cake batter and cream cheese layer are both very, very thick. This is what prevents a great deal of sinking/mixture and produces those pretty layers in the final product.
To sum up: Yes, I think this should be totally possible, but I can only offer suggestions, not actual experience with this precise cake here.
EDIT: Looking at the recipe, it already seems to be a fairly dense cheesecake-- no cream. The only liquid is one egg to hold things together, so you wouldn't need to change anything there, I don't think. The only reason there seems to be sinking and mixture is because of the way the apple is cut and the amount of it compared to the cheesecake. The apple layer is 1500+ grams, while the cheesecake layer is less than 1000. You'll still have to experiment, but I would think you could pretty easily cheat by using a thin layer of sliced apple.