No, Australia hasn't added a requirement that one needs to be tax resident in some country outside Australia to get out of their tax net.
Currently Australia has a few tests including the domicile test, which says that one has to have a permanent abode in some country to no longer be an Australian tax resident. It doesn't specify that one has to be a tax resident in the country of permanent abode, but normally (but not always) having a permenant abode somewhere means one becomes tax resident.
For people who have lived long term in Australia and want to leave, the proposed new Australian rules say that:
-if one gets a job that lasts at least 2 years outside Australia, one has accommodation in the place of employment, and one doesnt spend more than 45 days in Australia per year, then one is out of the tax net directly when leaving Australia.
-If one has spent less than 45 days in Australia per year for the two previous years, then one is out of the tax net the third year, assuming one spends less than 45 days that third year too.
In other words Australia never had an explicit requirement to be a tax resident abroad, and with the new rules tax residency abroad is even less of a factor. Note that if you are an entrepreneur and move out from Australia to say the UAE, you will still be an Australian tax resident for 2 years regardless of if you are a tax resident or not in the UAE. And then from the third year you will not be an Australian tax resident, again regardless of if you are a tax resident in the UAE.
This flowchart explains the new rules quite well:
https://www.exfin.com/files/general_materials/Proposed New Australian Tax Residency Rules Flowchart.pdf
Im actually not aware of any country that explicitly requires tax residency abroad to get out of the tax net. Possibly Spain is the closest, where i understand that in practice it is likely one has to show tax residency abroad.
But there are many cases where even if you are a tax resident abroad, you are still counted as a tax resident of the country you left. Like all the full on or quasi taxation by citizenship countries, or countries with anti tax haven rules. The by far most common case though is that you can move out, and the country you left doesnt care if you are a tax resident abroad or not.