"Vienen aquí cuando se manifiesta."
I find it hard to think of a situation in which the translation "...when there is a manifestation" or "... when it manifests" makes any sense at all. This sentence obviously requires a very loose translation that one can only find when the context is given. E.g. "... when it shows" or "... when it is shown" (w.r.t. a film) or "... when it gets worse" (w.r.t. cancer).
I was sincerely confused so I looked for the sentence in a context. This is what I came up with.
Apártense, soy médico.
- Déjelo en paz. No lo entiende.
00:09:17- Se está muriendo.
- Por supuesto que sí.
00:09:20Ha venido aquí para morir.
Vienen aquí cuando se manifiesta.
00:09:24Les ayudo a morir en paz.
Rodeados de su familia y amigos.
00:09:28¿Qué está diciendo?
Stand back, I'm a doctor.
- Leave him alone. You do not understand.
00:09:17 - He's dying.
- Of course I do.
00:09:20 He came here to die.
They come here when it manifests.
00:09:24 I help them die in peace.
Surrounded by their family and friends.
00:09:28 What are you saying?
Thanks for finally solving this mystery. I wonder why nobody thought of googling the exact sentence before. I can't find the English subtitles, but it seems clear now that "cuando se manifiesta" is originally an attempt to translate the very unusual English phrase "when it quickens". So not only is the supposedly correct translation wrong, but it's also virtually impossible to find the correct one without the original context. This sentence should simply be removed, or should be replaced by a sentence that makes sense and covers better whatever it is supposed to cover.
"They come here when there is a demonstration." makes sense. I have lived in a Communist country, and both before and after the regime such a sentence would have fit. "Manifestation" was actually the word adopted in the socialist language. "Se manifiesta" just translates to "there is a demonstration". "Here" could be the place of the demonstration or a cafe where people gather before or after the demonstration.
Concerning weird sentences in general, let's not forget that Duolingo is crowdsourcing the translation of Wikipedia articles. It is natural to expect all kinds of weird sentences from the Web. And, boy, are there many!