There is no such thing as a 1 month tourist visa. I suspect you’re referring to a 30 day visa exempt stamp that you got. Way back when exempt stamps were 30 days there wasn’t an issue for most opening an account.
In the past few months it’s become almost impossible to do so for anyone not on a long term visa.
Your experience 2 or 3 years ago is irrelevant these days.
Yes it can be done all online in Australia. Indeed it needs to be done in Australia (if that’s where you physically are). Sydney covers those residing in NSW. Canberra covers elsewhere.