A quickening occurs when the player levels up by gathering enough XP, or when a Rune of XP is cast on you or a monster. During a quickening, the quickened creature rises and emits bolts of lightning that damage all nearby creatures. Their stats are raised and they are also healed to maximum health in the process.
In a quickening for the player, both Red and the Minion are quickened. The lightning does not damage either of them, but will still hurt nearby monsters significantly. Monster quickenings are individual and will cause damage to the player and minion.