This page explains what to do at Marbule (Home World) in Chrono Cross: The Radical Dreamers Edition.
After borrowing the boat from Norris at the Home World version of Viper Manor, set sail for Marbule–the village of demi-humans towards the south-east.
Unlike its counterpart in Another World, this version of Marbule is devoid of people, save for two very brave (or stupid) explorers. Instead, it’s infested by spectral monsters that don’t seem to be of this world. You can’t touch them and they can’t touch you, though.
Walk around Marbule until you find Toma the explorer. Speak to him to gain information about what’s happened to Marbule, the Dead Sea, etc. After interrogating him, enter the house by the entrance and sleep in the bed.
During the night, you’ll hear voices… Wake up and leave the house. Outside, head towards the bridge near the center of the village. A woman will dive into the water and swim away.
Toma will then come along and tell you to go back to sleep. He’ll mention visiting the S.S. Zelbess and speaking to Fargo, its captain. The next day, when you exit the house, Irenes–the mermaid who you glimpsed last night–will “join” you, as you travel to the S.S. Zelbess.