Ballinascreen councillor Brian McGuigan, who witnessed the rescue, described the rainfall in the Sperrins as "exceptional."
The Sinn Féin councillor said the family's house is on the edge of the River Moyola at River Road outside the town.
"All the rain water came off the mountain and built-up as it had nowhere to go and the river was not able to take it," he said. "The water must have come in (to the house) very fast and the family ran upstairs."
The banks of the river was breached and the water is understood to have flooded the ground floor of the two-storey property.
The Northern Ireland Fire & Rescue Service were alerted and rescued the trapped family using a dinghy.
Councillor McGuigan said thankfully noone was hurt but the bottom floor of the house was badly damaged by the flood water.
He said there had been a lot of flooding in the area, and he had been out most of the day with sandbags for properties and ensuring roads are kept open.
"This is not normal rain any more and when it comes down people have to be prepared and this is what we are going to be up against," he continued.
"This was a major incident this morning and this family who have been living in the house for at least 25 years will have to make a difficult decision about where they are going to do in the future."
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