What happens if Bringer of Dreams and Nightmares uses the threshold effect of Cast Down into the Briny Deep?

What happens if Bringer of Dreams and Nightmares uses the threshold effect of Cast Down into the Briny Deep?

Per its special rule, Bringer of Dreams and Nightmares will not destroy the targeted board, nor anything on the targeted board other than its own Presence. Since all the Invaders there would be destroyed, they instead are pushed and/or generate Fear, per Bringer of Dreams and Nightmares' usual rules.