What date and time definition is used for the second leg of a flight?
You are looking at two different planes.

This is the flight from London to Singapore, which departed on 17th of August, on flightaware.com:

The dates and times are local, meaning the flight departed 2019-08-17T21:11:00Z (UTC) and landed 2019-08-18T10:23:00Z.

Before this flight even took off, another 777 departed Singapore headed for Sydney:

The flight departed 2019-08-17T11:56:00Z and landed 2019-08-17T19:09:00Z.

The plane which landed in Singapore on the 18th of August also continued to Sydney later that day: