Taii Wakeen’s first ability doesn’t care about any damage already marked on a creature. It just cares about whether the noncombat damage dealt to a creature by a source you control was equal to that creature’s toughness.

The additional X damage is dealt by the same source as the original source of damage. The damage isn’t dealt by Taii Wakeen unless Taii Wakeen is the original source of damage.

If another effect modifies how much damage a source would deal, including preventing some of it, the player being dealt damage or the controller of the permanent being dealt damage chooses an order in which to apply those effects. If all of the damage is prevented, Taii Wakeen’s effect no longer applies.