All of the examples here of transits that I am aware of (India, South Africa and onwards etc) were where the person booked two tickets without a visa for the midpoint or anyway to legally stay in that country - airline only has a contract to that mid point where there was no legal reason to stay. If it was booked as one ticket in each situation they would have been fine.

Your situation is slightly different. They will be allowed to transit/stop over under a VFTF for 96 hours which is allowed if you travel to an eligible "third country", Which Australia is one of the short list of allowed examples under VFTF, both for inbound and outbound travel to SIN. You also have to ensure on the return that your ticket is back to your "home country"
https://www.ica.gov.sg/enter-transit...ansit-facility

The question that should come up, is as your ticket is separate, they should ask to see the onward travel to Australia on the outbound and back to your "home country" on the inbound - within 96 hours. And confirm that your next flight is either AU or your home country and you should be fine.

Lots of shoulds and I have no experience with VFTFs, but on first principles you should be fine. And expect that online checkin will not work.

Someone else will soon come and either confirm or correct the above :-)

KF