Important:
This answer is based on tax law year ending 28 February 2017.
Answer:
Your interpretation is not 100% correct. The taxing rights are, in this instance, determined in the agreement for the avoidance of double taxation between the RSA and Australia. It would deal with the specific ‘incomes’ where there is a source / resident clash. Specific to your request however is where the person is a tax resident – you sate there is dual residency. That is dealt with in Article 4 of the treaty and reads as follows:
“3. Where by reason of the preceding provisions of this Article a person, being an individual, is a resident of both Contracting States, then the person’s status shall be determined as follows:
the individual shall be deemed to be a resident only of the State in which a permanent home is available to that individual; but if a permanent home is available in both States, or in neither of them, that individual shall be deemed to be a resident only of the State with which the individual’s personal and economic relations are closer (centre of vital interests);
if the State in which the centre of vital interests is situated cannot be determined, the individual shall be deemed to be a resident only of the State of which that individual is a national;
if the individual is a national of both States or of neither of them, the competent authorities of the Contracting States shall endeavour to resolve the question by mutual agreement.”
The “the preceding provisions of this Article” refer to paragraphs 1 and 2 of Article 4.