I tested this on your site with Oceania and Asia.
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Now I see that it does not for hidden link, as example.
Now, the ShortCode order attribute accepts only two values:
asc, desc.
The code uses ksort() to sort the output.
This is a function that allows to sort alphabetically by key, but holding the array structure.
So for example, if you have an array array("d"=>"lemon", "a"=>"orange", "b"=>"banana", "c"=>"apple");, ksort() will output:
a = orange
b = banana
c = apple
d = lemon
This means for our case here, if you have a Parent and Child term structure, it will order them asc or desc alphabetically holding the structure, means first order the parents alphabetically then their Childs, separately.
This would result in something like this:
- A letter parent
-- A letter child
-- B letter child
- B letter parent
-- A letter child
-- B letter child
Etc.
And that seems to work just fine for some of your terms, not for others.
And I see now why this works on my local, but not on your site.
As I stated earlier, disabling all plugins made it work.
I suspect you use a Plugin to manipulate Terms.
See in the single Post edit screen for example:
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The Viagens taxonomy is clearly not native, it states that it made a child term to be "Primary".
That would then somehow match the problems we get on the front end - it changes the parent term.
Please try this again with no plugins. Eventually you need to reserve those posts, I am not sure how this specific feature is added to the posts, but it is not native to WordPress or Toolset, and it might interfere with what WordPress reads of it.
In fact, the posts that work fine have no such "primary" term