You can reveal an enchantment at any time, as long as you are not interrupting an step. Such as the 3 steps when casting a spell, or the multiple steps when attacking. Going in between steps is fine. An example was posted in a different thread about the enchantment that made it cost mana to move. So the target of the enchantment declared he was acting by turning over his action counter, but before he made his move action, so in between steps, the controller of the enchantment could reveal it to penalize the forthcoming movement.
For quick cast actions, this would be the same. There is a space between declaring the use of the action (flipping over the tile) and the beginning of the spell casting steps that you could use to reveal your enchantment.
