Combat like this without reserve cavalry likely devolved into dismounted melee immediately after the first charge. They would have started mounted, charged with lances, became embroiled in close combat, eventually dismounting or being pulled off, then melee combat on foot.

The squire in question probably broke ranks and ran off and mounted his steed and then flanked his opens at full charge and just ran them over. That’s usually the job of reserve cavalry to smash formations of foot soldiers but they agreed to not have any reserves so it could be considered against the terms they agreed to even if he was taking part in the fight from the start.