The 48 Venezuelan migrants flown to Martha’s Vineyard by Florida’s governor, Ron DeSantis, this week were told they were going to Boston and given incorrect information about their legal obligations as asylum seekers, according to lawyers who interviewed them Friday.

“They were told that they would have a job and they would have housing,” said Elizabeth Folcarelli, who leads Martha’s Vineyard Community Services.

Julio Henriquez, an attorney who met with several migrants, said they “had no idea of where they were going or where they were.”

The two flights stopped in the Florida Panhandle en route to Martha’s Vineyard, Mr. Henriquez said. While on board, migrants received brochures and maps of Massachusetts and an unsigned letter telling them to notify the U.S. Citizenship and Immigration Services of address changes.

In reality, Mr. Henriquez said, U.S. Immigration and Customs Enforcement is actually responsible for tracking migrants. The guidance in the letter “is terrible advice,” he said.

Many of the immigrants have appointments with ICE on Monday in San Antonio. Others were ordered to report to immigration authorities in two weeks to three months in cities including Philadelphia and Washington.

U.S. officials told the immigration attorneys that the required check-ins would be postponed, Henriquez said. Homeland Security officials didn’t immediately respond to a request for comment Friday.

In San Antonio, a Latina woman approached the migrants at a city-run shelter and put them up at a nearby La Quinta Inn, where she visited daily with food and gift cards, Henriquez said.

The woman, who introduced herself to migrants as Perla, promised jobs, housing and support for their immigration cases, said Oren Sellstrom of Lawyers for Civil Rights, which offered free consultations.

One of the migrants, Pedro Luis Torrelaba, 36, said he was promised work, food and housing. He thought he was going to New York.

“I am not a victim,” he said Friday, expressing gratitude to residents of Martha’s Vineyard for their hospitality. “I simply feel misled because they told a lie and it has come to nothing.”

The migrants were being moved voluntarily Friday to a military base on nearby Cape Cod.

Mr. DeSantis said Friday that most migrants intended to come to Florida and that the trip to Martha’s Vineyard was voluntary. He did not address the migrants’ claims that they were told they were going elsewhere.

Florida’s governor defended picking up migrants in Texas and vowed to continue transportation to immigrant-friendly “sanctuary” jurisdictions.

“Our view is that you’ve got to deal with it at the source, and if they’re intending to come to Florida or many of them are intending to come to Florida, that’s our best way to make sure they end up in a sanctuary,” he said.

Texas has bused about 8,000 migrants to Washington since April, including more than 100 Thursday to Vice President Kamala Harris’ home. It also has bused about 2,200 to New York and 300 to Chicago.

Arizona has bused more than 1,800 migrants to Washington since May, but has kept officials on the receiving end informed of the plans. The city of El Paso, Texas, has sent at least 1,135 migrants on 28 buses to New York since August 23 and, like Arizona, shares passenger rosters and other information.

Volunteer groups often wait hours for buses arriving from Texas in a designated space of Manhattan’s Port Authority Bus Terminal.

“It’s a problem because we don’t know when the buses are coming, how many buses are coming, if anyone on these buses has medical conditions that they will need help with,” said the commissioner of the New York City Mayor’s Office of Immigrant Affairs, Manuel Castro. “We at least want to know that so that we can best help people as they arrive.”