Does Yellow Mold tick at 0 HP

If a creature got hit by a cloud of Yellow Mold (DMG p105) and it fails it’s saving throw it becomes poisoned.

While poisoned in this way, the creature takes 5 (1d10) poison damage at the start of each of its turns.

What happens if this creature drops to 0 hit points? Does it still takes the poison damage each round and for that dies after 3 rounds?