I looked in to the reigns of the two Túrin Stewards. The first had a pretty uneventful reign, as one of the Stewards in the middle of the Watchful Peace. The second, though: he was the son of Thorondir. During Thorondir’s reign was when the White Tree began to die. So that’s some apocalyptic stuff. Túrin II gives birth to Turgon. During Túrin II and Turgon’s reign, Mordor begins attacking Ithilien regularly, and Sauron reoccupies Mordor two years before the death of Turgon. Upon the accession of Denethor II’s father, Ecthelion II, Saruman claims Orthanc. So yes, there is much apocalypse about these Stewards, and reasons for Gondor to think apocalyptically.