It's not a great wording. Even the intent is not so great (it presumes too much about the game flow to be useful). Using it after a hit is probably OK. The power gain for the bard will be marginal. There weren't a whole lot of situations where it makes a difference and the outcome is so randomized that even there, it doesn't always do anything.
Arguably the provision "after seeing the roll" is meant to imply "after the attack is declared but before the roll is made". But that doesn't really matter for the results.
I imagine the "see the die" requirement is for the aforementioned 2s and 19s so you can know not to waste the inspiration. But I don't see that working well in play.
Thoughts?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.