The monk's Deflect Missiles feature description says (PHB, pg. 78):
Starting at 3rd level, you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack.
I take this to mean that the player controlling the monk gets to decide whether or not to use Deflect Missiles after they know whether or not the attack hits.
When you do so, the damage you take from the attack is reduced by 1d10 + your Dexterity modifier + your monk level.
Does the monk's player get to know the damage before they decide to use Deflect Missiles? Or is damage is rolled after they choose to use the feature?