The correct answer to this open question is the following.
If I use my knowledge of the Bering land bridge to understanding the connection between these two cultures, I can say that the Australian and New Zeland Indian tribes are closely connected because they could have come from the same land and emigrated to these new territories after a catastrophic event that made them leave their native lands. It could have been a climate change event, the rise of the oceans' level, an earthquake, or a volcano explosion, as has happened many times in the history of humanity.
Many historians and anthropologists believe that these Polynesian people could have lived in the mysterious continent of Lemuria or Mu, which sunk thousands and thousands of years ago. Some of those native people sailed to different territories. Some theories say that people from that continent sailed to what today is the Hawaiian Islands. Others sailed to Rapa Nui (Easter Island), and many others sailed to Tahiti, Australia, and New Zeland.