I'm not native to Taiwan, nor do I have any knowledge of Taiwanese Mandarin. Hence it could be that all is as intended. My observation:
NumberFormat format = NumberFormat.getCurrencyInstance(Locale.TAIWAN);
format.setCurrency(Currency.getInstance("TWD"));
System.out.println(format.format(1600));
Results in $1,600.00. This might indicate to a reader the US Dollar, not the new Taiwan dollar (TWD). But TWD uses as symbol NT$, hence I would assume the correct result to be NT$ 1,600.00. Debugging indicates that the NumberFormat construction evaluates to a Symbol set in which $ is a default prefix - but before digging too much into details. Is this the intended behavior?
Seems to be intended. Based on the list of Currency symbols on Wikipedia, most of the different dollar currencies like Can$/C$ (Canadian dollar) or NT$/元/圓 (New Taiwan Dollar) (see third column of the table) still use simply $ as actual symbol (see first column of the table).
There are some currencies where a letter + $ is actually the symbol, like the Nicaraguan córdoba for example with C$, for which the Java symbol and formatting is as expected with C$: try it online.