Hurricane Irma has sustained top winds of almost 180mph and at least ten people have been killed so far.
Daniel Collins from Paisley is visiting the Dominican Republic with his wife Heather.
He said: “Initially we were told not to panic because they weren’t sure which route the storm will take.
“We were obviously told to stay indoors – but there hasn’t really been any mention of being evacuated.
“At first we thought it was just going to be a rainy day in Glasgow, but then it suddenly got worse and it has been really scary.
“The wind was been absolutely ferocious. It’s the noise of it that gets you more than anything – it’s been chaos.”
Martin McCreadie from Giffnock in East Renfrewshire, is staying on the island of Cayo Coco, near Cuba with his wife and four-year-old daughter.
Mr McCreadie yesterday hit out at Thomas Cook for delays in being evacuated from the island.
He said: “We were waiting to be evacuated today. There’s a Force Five hurricane on its way, it’s absolutely terrifying.
“We have been told that there’s a bus coming to take us to Varedero, which is a nine-hour journey and it doesn’t look much safer than where we are. Then they are going to fly us out from Havana.”
He added: “There’s been no communication from Thomas Cook, it’s been absolutely ludicrous.
“There’s no logic and there are about 35 to 40 of us sat in the lobby with our luggage, waiting for this bus to come back.
“We were told there was a window to evacuate but that has passed. It’s a really difficult situation and people back home are really scared.”
Thomas Cook said it was “closely monitoring” the situation as it develops.
A spokesman added: “The safety of our customers is always our first priority.”
Irma is expected to reach Cuba before passing over the US state of Florida on Saturday.
The hurricane was already affected around 1.2 million people, while the Red Cross estimates that 26 million could be caught up in the storm.
Evacuation orders are intensifying across Florida as local officials try to get the most vulnerable populations to move ahead of Hurricane Irma’s arrival.
Billionaire Richard Branson said he and his staff rode out of Hurricane Irma on his private Caribbean island without suffering any injuries, but that the area was heavily damaged.
The first islands to be hit by Irma were Barbuda and Antigua. French officials believe that at least four people have died in Saint-Martin and more than 50 people have been injured.
The Cuban civil defensive agency is preparing people on the northern coast of the island’s eastern provinces for a sideswipe from the storm in the hours ahead.
Santiago province has opened 125 evacuation centres that can hold 38,000 people. Another 20,000 people can take refuge with neighbours and family in safer zones.