There are a number of explanations that have been provided for it. It seems that which is correct depends on the location and storyteller.
Attempting to come to a single conclusion that can be generally agreed upon seems to be impossible:
The attempt to find a tradition what is recognized by the whole tribal community has unfortunately come to nothing.
They seem to be able to move independently. According to a wondjina artist, they walk, and travel, as the rain does.
Long Watty says Wandjina came from ground, live in clouds, rain comes after he lift cloud, rain go down. Rain travels as the Wandjina walks - Wandjina travels. Then Wandjina goes down with rain (or as rain?) and into ground ...