This is a tricky thing Let's go step by step!
What does Way of the Crane do?
+1k1 Attack Rolls and Focus Rolls, as well as in rounds after exiting Center Stance.
When do Attack Rolls happen?
The rules are in the L5R Core Rules on page 82 (emphasis mine):
Attack & Defense
Any attack a character makes against an opponent requires a
roll, typically a Skill Roll that includes a Weapon Skill as one
of its components. Attacks may be melee or ranged in nature,
depending upon the weapon being used. These rolls are made
using the rules included for Skill Rolls above, and the result
of an attack roll is compared to the opponent’s Armor TN. [...] If the result
of the attack roll meets or exceeds the target’s Armor TN, then
the attack was successful and the opponent was struck with
the weapon in question. Damage must now be rolled.
Penalties or bonuses may be applied to attack rolls for a
variety of reasons. [...]
[...] The Wounds inflicted by an attack fill up
these Wound Ranks in order[...]
When do Focus Rolls happen?
Focus rolls only happen during Iaijutsu duels as step 2 after the assessment roll.
What does happen after center Stance?
With Way of the Crane, you get +10 Initiative for that round and +1k1+Void Ring on any one roll (standard) and +1k1 on all attack rolls (Way of the Crane).
Attacks are an action that first demands a successful attack roll which then demands to roll for damage, a distinct and separate roll, that does not apply the same modifiers. You don't apply Way of the Crane on rolls for damage, but you could apply the standard bonus from Center Stance to a damage roll - provided you hit.