It may have first claim taxation rights on taxable incomes but income disbursed 'untaxed' then falls into the taxable rights of the other jurisdiction. Thats the whole point, they dont tax super at payout. Theres no other polite way to say it but I would feel you simply dont fully understand the language of the DTA as a layman or have had bad advice. I am a cross border payroll and income tax specialist, mostly UK EU but understanding and exploiting DTAs is what Ihave done for over 3 decades now.
This is very common for Oz pension recipients living in EU or UK, the payout isnt taxed in Australia but they now live in a place where that 'benefit' of no tax no longer applies and they pay UK or EU income tax on the super.
I know that many (all !!) of the major expat cross border tax specialists operating in Thailand that I have spoken with, have said that if they pursue it by the book Oz super is now clearly Thai taxable.
They are untaxed at disbursement.. And if your Thai tax resident in any tax year you import those funds they are untaxed income from Oz.. Thailand specificially includes pensions as taxable income at time of receipt (and importation to Thailand).
You dont get to simply say I am an oz tax resident and dont pay it where I live, BOTH tax regimes can have competing claims. There are plenty of situations under DTAs where a source country might get the first layer (eg 0 - 15%) and the second country get the layer from the lower band to the higher band (in that case 15 - 35). Thats normal cross border tax stuff.
Simply believing 'I am an australian hence my tax is based on Aussie tax rules' is totally not how it works, BOTH regimes can have claims tho under DTAs it is usually a primary claim.
THIS is one of the biggest unknowns right now and one the tax office is noticably silent on clarifying.
Up to now, and still according to some (many / most) only those with a LIABILITY must file. But some tax advisors are now saying anyone with assessable income must file (so that would include everyone with DTA protected income or similar).
There is a huge difference between these 2 positions.
Secondly anyone who fails to declare a liability that they determine is open to a 100% fne on top of the liability.
A friend was importing goods, there was a fee that was a fixed price but inspection and a bigger fee for a (claimed) 'don't open' the container. Can you imagine what comes in to the country on the 'don't look' fee??
Same guy imported a pinball machine (considered a gaming machine like fruities) and he paid for it to be 'illuminated furniture' for about 30k 🤣🤣
Premium items only thing to consider.. Hard to obtain and the import costs, inefficient dealer / supply chains, and small local market make the prices crazy high.
Generally I just pay the extra baggage fees and hand carry everything or book it as sporting goods on the plane.. Some of my airport arrivals have been comical.