Arial Black
Adventurer
Where are you getting that it happens between the attack being determined it's a successful hit and the effects being applied?
From the way UD handles what it does handle: damage.
UD must kick in before damage is applied, because if it didn't then the damage would be applied and then some of it would heal. If UD was healing it would be called out as healing in the text so it could interact with other healing rules, and it wouldn't be 'Uncanny Dodge' but 'Uncanny Healing'; not that such an ability would make any sense for a rogue...
It would also make UD unusable if the un-halved damage would leave the rogue at zero hit points, and it doesn't work that way. UD means that the rogue never took half of that damage at all!
Therefore, UD works between 'successful hit' and 'apply effects of hit'.
More to the point, how can UD halve damage that hasn't happened yet?
It certainly cannot halve damage that has already been taken!