A section of the retaining wall, described as six metres (20ft) tall, collapsed at about 22.30 GMT on Saturday in Berw Road, Pontypridd.
Residents described a noise "like thunder" and said it was lucky nobody was killed. Four homes were evacuated.
Rhondda Cynon Taff council said the wall was the residents' responsibility.
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Just as we were starting to run down the stairs you could hear the whole thing crash and it was like thunder”End Quote Craig Stewart However, it said it was working with them to make the area safe, and said it would "investigate the history of the issue".
Some residents claim fears about the safety of the wall had previously been reported to the council.
Resident Craig Stewart had to flee his home with his partner and seven-month-old baby.
He said: "I was in the living room. I started hearing noises outside.
"I went upstairs to look out of the window to see what the noise was.
"The last noise I heard was creaking wood, so I knew it was the support that we've got up, because it's the only wood around here.
"So then I knew the wall was putting pressure on it."
He said he and his partner left the house with their baby, adding: "Just as we were starting to run down the stairs you could hear the whole thing crash and it was like thunder."
He said his extension "could fall down any minute" and a neighbour's kitchen had "completely caved in".
"Anybody stood in there would've been dead basically," he added.
Mr Stewart's father, David, said the terrace included about 10 miners' cottages.
Part of the collapsed wall in Pontypridd He said: "There's a black expanse of rubble and earth.
"The rubble is up to the bedroom windows in some cases, and one kitchen has disappeared. How nobody was killed, I don't know."
'Massive bang'Another resident, Salman Khan, said his wife and son were at home when they heard a "massive bang". He said his family had been "very lucky".
South Wales Fire and Rescue Service said it was called at 22:57 GMT on Saturday, and left the scene at 00:18 on Sunday.
Continue reading the main storyThe council will also be investigating the history of the issue with the residents so that the situation can be resolved”End Quote Rhondda Cynon Taf Council A spokeswoman said four homes were evacuated - numbers 21-24 - and a Rhondda Cynon Taff (RCT) council surveyor was assessing the structural damage.
In a statement, RCT council said was alerted to the collapsed wall on Sunday, following "severe weather that the county borough has been experiencing".
It added: "As a result a number of residents have been evacuated from their homes whilst the council liaise with residents to make the area safe.
"However this wall remains the responsibility of the residents and is a private matter, but the council will continue to work with those affected to make the area safe in the short-term.
"The council will also be investigating the history of the issue with the residents so that the situation can be resolved."
Elsewhere, 11 homes were evacuated overnight in Ystalyfera in the Swansea Valley after a landslip due to flooding.
Affected residents spent the night in a nearby leisure centre, and South Wales Fire and Rescue Service said four homes remained evacuated on Sunday.
Arriva Trains Wales (ATW) said flooding disrupted services between Cardiff Central and Bridgend, and Caersws and Machynlleth in Powys.
