Certain damage kickers are put into effect at the attacker's option after it is determined that an attack is a hit. Examples include:
- The Divine Smite of paladins and of several cleric domains
- The Battle Master's Trip Attack
- The Combat Inspiration feature of the College of Valor bard
- Expending charges from several magic staves, including the Staff of Power, Staff of Striking, and Staff of Withering
The rules on a critical hit seem pretty clear (PHB. 196):
Roll all of the attack’s damage dice twice and add them together.…
… If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.
It seems clear that (a) the player decides to apply the kicker after seeing the die roll, and (b) "all of the attack's damage dice" includes the kicker. But this gives the player quite an advantage to choose to apply a damage kicker on a known critical hit, so I am seeking to confirm (or correct) my understanding.
Can the attacker wait to add optional damage dice until after seeing if the roll is a critical, knowing that the additional damage dice will be doubled?