Long comment (too long for a comment) regarding my preceding comment's link to
I think that might be analogous to what you're trying to think about in the following way, which is analogous in some ways, but very different in other ways...
You introduce C as a "cause" with mutually exclusive possible effects Y and Z. Instead, think of that cause C as a preparation procedure that prepares an entangled system (see that paper's title) with components Y and Z. And let's use the usual example that Y and Z are electrons, prepared by C such that the total system has spin-0, with one component spin +1/2 and the other -1/2.
Then these two "effects" are indeed mutually exclusive, but C has prepared them both. And that's what leads to some very weird causality issues.
Subsequent measurements of Y or Z's spin are non-deterministic: measurement of either gives you a 50-50 chance of a +1/2 outcome (and ditto for a -1/2 outcome). However, once you've measured either one of them, the outcome of a >>subsequent<< measurement of the other is guaranteed. If the first outcome is, say, +1/2, then the second outcome is always -1/2. So you might be tempted to say that the first "caused" the second.
But note how I emphasized >>subsequent<<. That implies you can know that one measurement occurred before the other. However, before performing either measurement, you can separate the two Y and Z electrons by a large distance d, and then perform both measurements almost simultaneously, by a time difference t such that d>ct (c the speed of light).
That's called a space-like separation, and means there's no possible communication between the two measurement events. So one cannot cause the other. People who don't want to believe that suggest faster-than-light communication. But that's not even the worst of their troubles.
What's really worst is that for space-like separated events, one observer can see one event occurring before the other, whereas another observer can see it the other-way-round. There's no such thing as my previously-emphasized >>subsequent<<. So you can't possibly say one event caused the other, because you can't even say which one came first. And this little conundrum isn't just theoretical; it's been experimentally verified time-after-time (starting in the early 1980's with Alain Aspect's famous experiments).
So what can you say??? The only thing that caused anything is the original C preparation event (it's in the unambiguous past, aka past light cone, of both Y and Z). But what did C "cause"?... the subsequent Y- and Z-measurement outcomes are non-deterministic, so C can't possibly have caused them. What C did cause is the correlation between them.
So how can you cause a correlation without causing the correlated events??? That remains an unanswered question. This space-time order-of-events confusion gives an entirely more subtle connotation to the idea of causality, with mathematical correlations themselves as "things" that can be "caused". So, rather than your contrived situation, I'd suggest you instead try focusing on the interpretation of these very concrete experimentally verified phenomena. Reality's a whole lot more mysterious and fascinating than fantasy.