"Dodge: When this unit is engaged by an opposing unit, prevent damage dealt to this unit equal to the number of rolled skill dice that do not deal damage."
Dice that deal damage must deal damage to a unit in the engage in which it was rolled. Damage is prevented for each die that does not deal damage that engage. The damage does not need to be resolved against the enemy with dodge - as long as the die deals damage to any unit within that engage, it counts as dealing damage.
Since Dodge looks at the results of your full dice roll, resolving this skill requires you to decide what you are doing with all of the damage-dealing dice you roll that engage.
A die that deals damage after the engage (even if later that same turn), or adds a status effect that deals damage, or gives tenacity that is used to deal damage, is not considered to deal damage.