Legally, you're here on a tourist visa, so that means you can't work here, period.
While it's technically possible to open a bank account here and/or get paid into your family member's account, this has the potential to land you/them in hot water if you're busted for working illegally, so the wise thing to do would be to get paid to Australia.
Now, whether or not you'll be busted is an entirely different question, but Immigration
will start asking hard questions the next time you need to renew your visa, because nobody stays in Singapore for half a year on holiday...
