As you say, this is about poetic/quasi-magical causality (examples—see below). Almost the entire point is that it is not about luck. It is somewhere between science and destiny. Here, you are on precisely the wrong end of the mechanisms that always get Luke and Leia to where they need to be, even if they have just done something amazingly stupid while also failing even to notice the problem.
These are mechanisms, not luck, and for you they work differently.
The most common expression for this in UK English is Sod’s Law. Wikipedia defines it rather inadequately (4 April 2016, and also confuses it with Murphy’s Law), thus:
Sod’s law is a name for the axiom that ‘if something can go wrong, it
will’, with the further addendum, in British culture, that it will
happen at ‘the worst possible time’. This may simply be construed,
again in British culture, as ‘hope for the best, expect the worst’.
That definition ignores the most important aspect of Sod’s Law.
In real usage, Sod’s Law always reflects the further observation that whatever you do to prepare, your efforts will be thwarted with incredible efficiency. You are basically, personally doomed. You could do exactly what everyone else is doing perfectly successfully, and yet for you it will still go impressively wrong.
In your example, you very carefully observed weather conditions for six days, made sensible predictions and took appropriate action. And then, precisely as you put it (but my emphasis):
It rains because you did not have your umbrella (yes, assume you are
magical and can control the rain by bringing/not bringing an umbrella,
but that you don’t know about this mysterious power).
You are right: you made it rain by leaving your umbrella behind—so it isn't really magic at all. It’s an effect that you can test and replicate scientifically (although that would probably go wrong as well...). It does increasingly feel like magic, though, the more often it happens.
Not only that, but also... everyone else is fine: they either brought an umbrella in this time (perhaps to take to the official umbrella dump, in view of the weather); or for some reason (that doesn’t include you) they just aren’t going outside today.
I have been known to point out that I can control the weather just by getting my bike out on what seemed to be a lovely day; or that I could control the direction of the wind (many successive times, until giving up the effort) simply by trying to light a cigarette. Like a good modern scientist I would try to suggest that I was joking about bad luck, while being unable to shake this nagging little worry that I was being in some way targeted with a consistency way beyond statistical randomness.
Not everything will go wrong: that’s Murphy’s alarmingly simplistic and fairly unhelpful little Law.
No, under Sod’s Law, the stuff that goes wrong is just anything mission-critical for which I thought I had prepared adequately. It makes me try harder next time... and yet, somehow, some new thing then destroys all my efforts all over again.
EDIT
I just found a rather nice little discussion of these two Laws by Michael Scannell:
If things only go wrong when they can, you can make sure they don’t.
Obviously, if things can’t go wrong, they won’t. Murphy’s law becomes
an incitement to be more careful: a forceful, energetic, Yankee take
on things.
Sod’s law is quite different. My guess is that its origins are English
or Irish. It is essentially fatalistic. Sod’s law will operate however
careful and energetic you are. The best any of us can do is put up
with things—preferably with a wry smile.
EDIT 2
For literary input to this theme I would point to fantastic narratives. The two that I have in mind right now are both very useful examples of the opposite of Sod’s Law.
As I have mentioned, Star Wars (1977). It makes no difference how stupidly Luke and Leia act, or in what ignorance of the wider political/historical/military difficulties. At every turn, something will organise the world such that this ridiculous action gets them to a position where their mere presence will further a mission that they didn’t even know they were on. Under Sod’s Law, your life and efforts work pretty much the opposite way.
Larry Niven, Ringworld (1970). Frequently mistaken for a quintessential hard science fiction text (Niven is a splendid author, and has played fantasy/sf tricks like this a lot), this novel is really about how things might work if what we modern types pompously dismiss as ‘luck’ is in fact some kind of universal force or property. Absolutely everything that happens within this story (and for quite some centuries previously) is conducive to manoeuvring a certain character into the most perfect and appropriate situation. Again, under Sod’s Law, one’s experience is consistently similar-but-different...
Best Answer
An alternative saying to the good one suggested by @Dan Bron is:
When it rains, it pours