I believe you are correct Demetrios. As I recall, it was Caesar who was initially falling back. The Gauls had been fighting against their nature. They did not enjoy the guerilla tactics that had helped them survive against the better-disciplined and trained armies of the Romans. Vercingetorix wanted his men to strike the baggage trains and avoid a full pitched battle. The over zealous Gauls did not heed. They must have felt their superior numbers might alone lead to a decisive battle with their spirits running high.

The ensuing defeat turned the tide. Caesar's fresh victory left the enemy needing to regroup and he took advantage of the moment. The Gauls were not unified like the Romans. They were a disjointed force of volunteers from various tribes and did not have the same level of military training. Vercingetorix had to keep his men together and Alesia was considered impregnable.

Caesar's walls were attacked daily as they were built. Vercingetorix used the time to send out riders to their various tribes to organize a fresh army and bring relief. At the time he took the position, he probably never considered that Caesar would build a second wall, allowing the Romans to as well be placed under siege. As a military first, it was genius. Hail Caesar!