Cuba had previously reported a preliminary estimate of four dead in the floods that damaged crops and infrastructure, left many communities cut off and forced authorities to open sluice gates on reservoirs that reached bursting levels.
Alberto, the first named Atlantic storm of the 2018 season, scraped by Cuba's west coast before charging into the southern United States, but still brought heavy rain, Presstv reported.
That caused treatment ponds of waste at the Cienfuegos oil refinery to overflow, resulting in a spill of 12,000 cubic meters of oily water into the bay, state-run media reported.
In the western province of Pinar del Rio, the National Institute of Hydraulic Resource said it had rained three times more than the historic May median, bringing reservoirs to 92 percent of their capacity and collapsing more than 40 homes.
The island country's biggest reservoir, Zaza, in the Sancti-Spíritus Province in central Cuba, reached its second highest level on record, state-run media said.
The heavy rains this year stand in stark contrast with the previous three years of severe drought in Cuba that saw reservoirs drop below 40 percent capacity.
As the new hurricane season gets underway, parts of Cuba are still recovering from Hurricane Irma, which rampaged through the island over three days, killing at least 10 people last September.
US forecasters said last week they expected the 2018 Atlantic hurricane season to be near-normal to above-normal in number and intensity of storms.