She had locked herself out of her employer's apartment when she took out the garbage.
Panicking because she was mid-way through preparing dinner, she went to a neighbour's unit and asked to be let in.
She then tried climbing back into her employer's apartment from there. The flats are on the fifth storey.
Ms Mila, 29, did not make it. The domestic helper fell to her death at about 5.40pm yesterday at the Stadia condominium at Yio Chu Kang Road in Serangoon.
Mr Choo Y. K., 47, who works in sales, told The New Paper that the Filipino helper had worked for his parents for three years.
The elderly couple were not at home when it happened because they were out with Mr Choo's brother.
He said: "We didn't know what happened until I reached at around 6pm. I saw the police tents and later heard someone mention my parents' unit number and I realised that it was our maid."
He suspects she may have been worried because the frying pan had been left unattended.
Mr Choo shook his head and said: "She was so silly. She should have called one of us instead. It is such a pity."
The last they heard from the helper was in the afternoon, when she called Mr Choo's mother about preparing dinner.
"My mother told her not to cook too much because they had a heavy lunch," he said.
His parents were at his brother's apartment when The New Paper visited the scene.
He said: "They are very shocked. Something like this shouldn't have happened."
Mr Choo said he hopes the tragedy can serve to caution other helpers not to attempt such a risky move.
Referring to the unattended frying pan, he said: "Even if a fire had broken out, we could have just called for the fire engine."
A police spokesman said they received a call at 5.41pm yesterday. When they got there, they found the motionless body of a 29-year-old woman.
He said: "She was pronounced dead by paramedics at the scene. Police are investigating the unnatural death."