There is a difference between actions that are allowed to be taken in a given phase and actions that, by rule, must be done in a given phase.
Nothing in the rules for tapping/untapping mention a phase requirement. This is in contrast to both rules on bringing a character into play and "Resource Cards, Non-Event" rules.TAPPING AND CARD POSITIONS
Normally, during play, each of your cards is placed on the playing surface so that its top is towards your opponent and its bottom is towards you. During play certain cards must be "tapped" when they are used - this is a record keeping mechanism to keep track of card usage. To tap a card, rotate it 90° so that it is turned sideways - to untap a card, rotate it back 90° to its normal position. When one of your characters is wounded, his card is placed with its top towards you (i.e., rotated 180° from an untapped position). All restrictions to tapped characters also apply to wounded characters.
Rules for the Untap Phase enable untapping, but the rules for the untap phase are not the rules for untapping any more than the rules for the site phase are the rules for combat just because they mention facing an automatic-attack.