From what I heard it works fine on Android, but on iOS it works ok... as long as you have the app running in the foreground, and your phone unlocked, while out and about.
The only way to fix that would be to use this new API on iOS.
I wasn't one who downvoted but parent post was asking for source on whether this app is going to utilize the new APIs, specifically. According to your subsequent link, near the bottom, currently it's unclear:
"The Government will work with Google and Apple to investigate whether the new functionality announced by Google and Apple partnership is beneficial for the app performance"
The COVID Safe app was already released (although not fully functional on the server side yet) but the Google and Apple APIs are not available yet, so doesn't that mean that it isn't using the Google and Apple APIs? At least currently, any way.
According to the Australian COVIDSafe app's privacy policy, when you register for the app, after you successfully enter a PIN sent by SMS, it transmits the following info to the Australian authorities: your mobile phone number, the name you enter, the age range you enter, the postcode you enter. The reasons for each are explained in the policy. This data is stored in the cloud. I don't see why the registration info (I'm just talking about the registration info, not the Blutooth-related data) can't simply be entered later, or stored locally on the device and not uploaded until, when and if, the user volunteers to share their registration info with health authorities, e.g. as a result of being notified that someone that was near them has tested positive for COVID-19. If this info wasn't transmitted as part of setting up the app, I expect the uptake of the Australian COVIDSafe app would be significantly higher.
I am also still waiting for Australia to publish the source code for their COVIDSafe app...