Story highlights The U.S. Coast Guard says 12 Cubans were picked up at sea

They were taken aboard the "Disney Wonder" cruise ship

The suspected migrants will be handed over to authorities in Grand Cayman

(CNN) A Disney cruise ship stopped on its way to the Cayman Islands to pick up 12 suspected migrants southeast of Cuba, the U.S. Coast Guard said Sunday.

Disney Wonder was heading from Miami to Grand Cayman when the group of suspected migrants was spotted around 8 p.m. Saturday, according to a source with knowledge of the incident.

The migrants were brought aboard the boat, which boasts "11 decks overflowing with restaurants, pools, recreation and more."

Disney Wonder won for "best entertainment" and "best service" in the 2016 Cruisers' Choice Awards from CruiseCritic.com.

The 12 suspected migrants, who were all Cuban, were on a "rustic" vessel, U.S. Coast Guard 7th District spokesman Jon-Paul Rios said. "Rustic" is a term authorities use to describe dangerous, unseaworthy vessels, Rios said.

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The suspected migrants are being turned over to Grand Cayman authorities, Rios said.