I'm reading the rules currently and noticed that every movement where your model comes in a cube occupied by enemy gives this model a free fight action.
Every move action leads to free fight action in this case.
But what about climbing? If you climb into a cube occupied an opponent model, do you get a free fight action?
From pg. 25, "If the model moves into a cube containing an enemy model then they must Fight it immediately. This is true regardless of the cause of the move."
From pg. 28, "If a model moves into the same cube as an enemy model then it will Fight for free as part of that action. This happens whether the movement is intentional (such as a Move action) or unintentional (such as being blasted into a new cube by a booby trap). "
I think a Fight starts whenever an enemy model moves into a cube containing a friendly model. A fight ensues regardless of the action that brought the enemy model into the friendly model's cube.