William Morgan Southa(n/m)'s mother Louisa appears to have died in 1871, and his father Thomas Morgan Southa(n/m) in 1879, so both pre-deceased Horace, born over in NZ in 1882. It wouldn't be surprising if what he knew about his grandparents was rather shaky even if his father had told him the entire truth.
I understand your reluctance to make too big a jump, but given the fact that he'd been in prison in Australia, William may not have been particularly honest, particularly to his future in-laws. I find it hard to believe there were two of them floating around with the same name who were both about the same age, one who was in Australia up to 1874 and the other who appears out of thin air in NZ a couple of years later.
William Morgan (Australia version)'s criminal records, which can be seen by going to
http://access.prov.vic.gov.au , choosing "search by series", and then searching for Southam in 515, confirm his father as Thomas Morgan Southam, veterinary surgeon. It also says he has three sisters (two married in Australia and one living in NZ). He was released in August 1874, plenty of time to hop over to NZ and woo a nice young girl there.
One option, if you haven't yet: you could get the death certificate of Thomas in Victoria and see how the children are listed on it.
