Darby is only the fifth storm to hit the islands since 1949.
Central and southern Mexico has been hit by torrential downpours which have left many areas under water.
Hundreds of people have been evacuated from their homes and more rain is expected over the next few days as a tropical storm moves up the country’s west coast.
Residents in the city of Tuxtla Gutierrez, in the southern state of Chiapas, were badly affected after heavy rains caused widespread flooding on Saturday.
The floods left three people dead after the Sabinal River burst its banks, affecting dozens of communities. About 600 people were taken to shelters.
On Sunday, a similar scene unfolded further west along the Pacific coast in Acapulco, where hundreds of people were trapped in their homes after heavy rains caused the Sabana River to overflow.
Acapulco recorded 165mm of rain in just 24 hours compared to a September average of 349mm.
The city is in the state of Guerrero, which was hit by two tropical storms in 2013, leaving dozens of people dead.
A resident affected by the flooding said the Mexican government had not listened to locals since and that some issues that led to flooding remain unresolved.
Subsequent hours have seen the development of Tropical Storm Newton. The system is currently located around 200km to the southwest of the port city of Manzanillo in the state of Colima.
Newton is packing sustained winds of 75km/h and is expected to strengthen further during the next 36 hours. It could be near hurricane intensity when it approaches the extreme southern Baja California peninsula Tuesday morning.
Damaging winds, large surf and heavy seas are expected. Some parts could receive up to 300mm of rain by the middle of the week, producing life-threatening flash floods and mud slides especially in areas of mountainous terrain.