‘ And the Spirit of Yahweh came on him, and he judged Israel. And he went out to war, and Yahweh delivered Cushan-rishathaim, king of Aram-naharaim into his hand. And his hand prevailed against Cusham-rishathaim.'
He was seen as the man inspired by Yahweh who could help them and they called on him to become their leader. He would first begin to set to rights things that were wrong, including restoration of covenant obedience and the putting away of strange gods. This was all part of his being a Yahweh inspired man. Then he gathered together and prepared an army ready for the next tribute demand.
“And he went out to war, and Yahweh delivered Cushan-rishathaim, king of Aram-naharaim into his hand. And his hand prevailed against Cusham-rishathaim.” He would first withhold the tribute when the time for it came to be collected. Then Cushan-rishathaim would raise a punitive expedition to demand it, and Othniel met the expedition and totally defeated it. It is not necessary to assume that Cushan-rishathaim was captured, but he was sufficiently dealt with to prevent him from returning.
“The Spirit of Yahweh came on him.” This phrase appears again and again in Judges (Judges 6:34; Judges 11:29 - where it depicts Yahweh assisting a war leader and Judges 13:25; Judges 14:6; Judges 14:19; Judges 15:14 where it refers to Samson). It results from Israel ‘crying to Yahweh' (Judges 3:9; Judges 3:15; Judges 4:3; Judges 6:6-7; Judges 10:10) and is seen as a direct answer to their cry. The point is not that he had some vivid experience of Yahweh, but that Yahweh had clearly taken hold of him to restore Israel and bring about the defeat of the enemy. From now on it was to Yahweh that they looked (for a time), not Baal.