I do them for the challenge. They are fun mix ups of normal missions (The one I'm doing right now has it's own layout, which is a nice mix up.). They also make good candidates for expeditions, to make doing the same level more fun on top of the new enemies.
As for reward, they are the only place (that I know of) to get quality umbracite while on NG. The Quality Umbracite can be used to temper better skills on to your gear, so it's pretty good to have.
Slayer of Demons,Inquisitor,Ylissean Tactician,Kindred Hunter,Gray Warden,Dark Lord,Good Hunter,Chosen Undead,Nerevarine,Exile,Mugunghwa Investigator,Tremere Anarch,ESPer,Squad 7 Hero,Nohrian Prince,Arisen,God Eater,YoRHa Android,Tenno,Hope's Peak Dropout
I actually ran into that the other day. If the twilight mission has rotated out, you can't summon any visitors into it. Blue Graves still work though.
Slayer of Demons,Inquisitor,Ylissean Tactician,Kindred Hunter,Gray Warden,Dark Lord,Good Hunter,Chosen Undead,Nerevarine,Exile,Mugunghwa Investigator,Tremere Anarch,ESPer,Squad 7 Hero,Nohrian Prince,Arisen,God Eater,YoRHa Android,Tenno,Hope's Peak Dropout