The friend posted on her Facebook page she heard no alarms, but suddenly people were pushing and screaming to get out, Mrs Weekes said.
"There are reports the evacuation at the opposite end of the mall was okay and that there was alarms, but it doesn't appear to be consistent throughout he entire mall."
Mrs Weekes said her friend and her children were uninjured.
Mr Weekes said clearly there were still safety problems at the mall.
"The main thing is nobody was hurt (this time)."
He and his wife had always been concerned that problems were inherent in the mall in terms of fixtures, fittings and the design.
"They appear to have improved the evacuation procedure, but they don't appear to have managed to actually resolve the issues with the constructing and materials."
More than 70 people have commented about the fire on the Doha Mall Facebook page, with many calling for the mall to be demolished.
One person wrote: "Unbelievable to see this happen again. The mall should be closed down for good!"
Another said: "Bulldoze the place down and erect a memorial in remembrance (for) our children who died there on 28 May 2012..."
But one person, who was in the mall during the evacuation wrote: "I was here and the complete evacuation was super fast and fire trucks were already here... No injures appears yet and everything seems controlled..."
Meanwhile, a criminal hearing to determine responsibility for the Gympanzee deaths is continuing in Doha but has been beset with problems and delays, frustrating the bereaved families searching for answers.
It was postponed four times because the owners of the daycare centre failed to show up, and in January Mr Weekes voiced concerns over evidence, saying the judge and victims' families had not been presented with an independent report into the fire.
The report was produced in one week, after which all evidence on the mall was destroyed, he said.
In February the hearing revealed evidence the nursery was not licensed, and victims' families said they felt insulted and attacked by questions posed to them during the hearing.
Mr and Mrs Weekes revealed last week that they are expecting twins in August.