Hi Py,
This is my first post on Balipod - hopefully you'll find it helpful. Indonesia, like most other countries, uses a time test (of 183 days) and not citizenship to determine the residential status of an individual for tax purposes (which I’ll refer to as ‘residence’ in the following). So your physical presence in a country, not your citizenship, is what matters for tax purposes. If for some reason you apply the residence tests for two countries and find that you are resident in both, the tax treaty between those countries will resolve this matter using “tie breaker” rules, assigning you residence to only one of the two. Usually, citizenship is not the first consideration to take into account in determining someone’s resident status according to tie breaker rules. For example the Indonesia-US tax treaty uses permanent home as the first consideration in its tie breaker rule.
Where you have an income from Indonesia, the Indonesian Tax Office will (and has the right to by treaty) tax this income regardless of your residence status.
Let’s say you have the capability to move around between countries flexibly, so you can choose where you are considered as a resident for tax purposes. You then need to take into account lots of other factors such as the location of your assets, type of income received, from which country this income is arises, etc. It's complicated, and depends very much on your personal circumstances.
Matsalaeh: Since you are a resident in one country for tax purposes - let says it’s Australia - you need to report and pay tax on all of your income (from Australia and abroad) to the ATO. So you sum up of all your income then apply the Australian tax rate (let say it’s 30%). Assuming that you have already paid tax in Indonesia (on the income you received from Indonesia), then the ATO will allow this to be deducted as a foreign tax credit against your tax due in order to avoid double taxation.