if you are a non-resident for aus tax purposes, then the new rules don't apply to you.
But if you are an aus resident for tax purposes, then they will apply to you. this means that you pay aus tax at aus tax rates. you also pay foreign tax (i.e. sg tax) but you get an offset from the aus govt for this.
you can be an aus resident for tax purposes if you are working overseas. establishing that you are a non-aus tax resident comes down to a few diff factors, all geared at showing that you intend and your actions indicated that you have permanantly cut off ties with australia.
have a look at www.ato.gov.au
and search for a fact sheet they have re residency.
but i would seek tax advice from the ato or a tax professional to really make sure, cos it will have a lot of impact on you if you are coming to work in singapore and get paid according to sinagpore salary standards.
the budget announcement came out 2 days before i was due to come here and i panicked!