Rafael is the 17th named storm of the season.
The deadly storm surge feared for Tampa appears not to have materialized, though the situation in the area was still a major emergency.
Storm surge and hurricane watches were issued for Florida's Gulf Coast, and a hurricane warning was issued for parts of Mexico's Yucatan Peninsula.
Authorities warn that storm surges of up to 20 feet could also wreak catastrophic damage.
Helene became a tropical storm Tuesday in the western Caribbean Sea and caused flooding in the Cayman Islands.
Texas officials urged coastal residents to brace for a looming hit by Beryl, which was a tropical storm on Saturday but was expected to regain hurricane strength.
Hurricane warnings remained in effect for Grenada and St. Vincent as thousands of people hunkered down in homes and shelters.
Hurricane Beryl strengthened into what experts called an "extremely dangerous” Category 4 storm as it approached the southeast Caribbean.
Beryl strengthened into a hurricane Saturday as it churned toward the southeastern Caribbean, with forecasters warning it was expected to become a dangerous major storm before reaching Barbados late Sunday or early Monday.
An average Atlantic hurricane season produces 14 named storms, seven of them hurricanes and three major hurricanes.