Jimenez said the facility where she was held was in Tuxtla Gutierrez in the southern state of Chiapas.
She was taken there with the promise that she would be given a permit to remain in Mexico while seeking asylum in the United States.
Jimenez was actually notified that she had to leave the country, she added.
"It's a disgusting place," the 56-year-old woman said, describing conditions similar to those in Ciudad Juarez.
The tragedy there unfolded after a migrant lit a fire in apparent protest over deportations, according to authorities, who have accused immigration officials and guards of failing to even try to evacuate the migrants.
Arrest warrants have been issued against three officials, two private guards and a migrant who allegedly started the fire, as part of a homicide investigation.
Just a week earlier, Moises Chavez was held in the same cell, which he described as a smelly room where guards treat migrants with disdain.
"There are no fire extinguishers or smoke detectors, but there are cameras," the 41-year-old Nicaraguan told AFP.
It was the second time that Chavez had been taken to the National Institute of Migration facility, where the fire claimed the lives of 18 Guatemalans, seven Salvadorans, seven Venezuelans, six Hondurans and one Colombian.
Video surveillance footage appeared to show guards leaving the 68 detainees locked inside as flames spread and smoke filled the room.
Ostensibly, such facilities are service and accommodation centers for foreigners who cannot prove their legal stay in Mexico.
In reality "you're treated like a prisoner," said Yusleidy Garcia from Venezuela, who was detained in Ciudad Juarez, where women and men are held in separate places.
"It was cold at night. They take away all your belongings. In the cell where I was there were 150 people" of various nationalities, she said.
Such conditions are in sharp contrast with rules issued by the government in 2012 requiring adequate food, hygiene protocols and protection of people and property in the event of riots.
Migrants are not supposed to remain in temporary-stay centers like the one that caught fire for more than seven days.
Some are transferred to other immigration facilities -- where the stay must not exceed 15 days -- to resolve their situation and receive legal assistance, and may be deported.
Mexican immigration last year detained at least 281,149 people in "overcrowded" centers and deported at least 98,299 people, including unaccompanied children, Amnesty International said this week in an annual human rights report.
Following Monday's fire, the rights group called for "an end to the practices that have caused untold damage, including torture and cruel, inhuman and degrading treatment, to thousands of migrants who have passed through these centers."
"These facilities are not 'shelters,' but detention centers, and people are not 'housed' there, but deprived of their freedom," Amnesty said, alluding to statements by President Andres Manuel Lopez Obrador.
The United Nations office in Mexico noted that the Global Compact for Safe, Orderly and Regular Migration -- an intergovernmentally negotiated agreement -- outlaws arbitrary detentions and calls for legal detentions to be as short as possible.
Other international standards advocate alternatives to arrest, the UN said.
Jimenez's detention lasted for two days, following a long and dangerous journey during which she said she slept next to the bodies of migrants who died in the Darien jungle between Colombia and Panama.
Outraged at being locked up when she was only trying to regularize her status, she recounted asking an immigration official: "Is it a crime to migrate?"
"She turned her back on me and left," Jimenez said.
© Agence France-Presse