As I understand it, with the Australian app, after a positive diagnosis, it is the health department which will request permission from the person who has tested positive, to contact anyone (who has the app), to inform them that they have been in close contact with someone who has been diagnosed with the virus, so they can watch for symptoms, get tested and/or self isolate.
It is not up to people to admit that they have tested positive - it comes through the official health channels.
Currently, anyone who tests positive is interviewed to try to determine where they have been and who they may have been in contact with. The app makes this process easier.
The problem is those who are asymptomatic, anyone with false positives, false negatives and potentially people refusing to allow the heath dept to contact other people they have been in contact with. Still, if it is something that may help so that has to be a good thing.
I don’t know if it is true or not, but apparently the Chinese had a similar app which is apparently how they have been able to get back to apparent normality so quickly. I don’t know if that is or was compulsory for all citizens.