It's the same issue that happens for using Mastercard gift cards at Walmart (which makes sense because the HIGC uses the Maestro/Mastercard network for debit transactions).

There's a trick. After you swipe the gift card, you have to hit cancel on the monochrome screen (not the red physical button) quickly, before the cashier hits a key. The transaction won't cancel but will in fact bring up a screen that lets you select from a variety of payment methods and you select ATM/Debit.

You need to do this because unlike the Visa gift cards, the Mastercard/HIGCs aren't automatically recognized as debit. You're getting rejections because the machine is trying to run it as credit.