There is a Digimon Adventure 1 picture in one of the episodes, but the public seem to have forgotten previous Digimon appearances in the real world.
Toei Animation, the original production company that put out Digimon Adventures, is definitely advertising it as a sequel to the original stories.
The release of Digimon Adventure Tri is supposed to be their gift to Digimon fans for the fifteen year anniversary of the ending of the original show.
You mention that it seems the public has forgotten past Digimon appearances in the world but I don't think so. After their appearance and destruction of the airport and town the news reporter states that this serves as a reminder of their destructive power. The fact that this is a reminder proves that they've seen events like this before.