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A head's deploy ability is a triggered ability. When both players trigger an ability at the same time the active players abilities will complete before the defending player. A player may order their own simultaneous triggers how they wish. The player controlling Quake may order Quake's damage trigger and Quake's head's deploy trigger such that Quake's damage ability resolves first, and Quake's head second. If Octone's controller is the active player, they must use Octone's bounty trigger before the defending player resolves their heads deploy trigger. This answer is an update on the originally published answer in the Roundup
An important rule to remember: The game checks for a player controlling zero characters at all times. However, Head character's deploy ability includes the following: 'When that character is KO'ed, even if it was your last character, deploy this battlefield in bot mode.' This is why you don't lose if your last character, a Body with a head, gets KOed.