This statement is very far from the truth. Gift box currency is always in USD. I am not sure if it is based on the site's default currency but it is always in USD. This statement is just for the sake of answering a question without a bit of accuracy.
As you can see, currency is not always in USD (for AliDropship Original plugin):
but as for AliDropship Woo plugin, we have an issue here indeed, currency is not changing in Gift Box from USD to any other currency, even client changes currency on a website. We will consider to fix this issue in nearest future.