How do AD/AP boosts apply to abilities with long cast times, channels or animations?

For example: I'm playing Janna in bot lane with Caitlyn. Caitlyn begins channeling Ace in the Hole to finish off an enemy. Will the AD buff from my Eye of the Storm apply extra damage to Caitlyn's ultimate if I cast at after she begins channeling? Similarly, if I see Caitlyn rev up to shoot Piltover Peacemaker, can I boost her AD after the animation begins? (If I remember correctly, Piltover Peacemaker has a quick cast time, but the spell animation is rather long, so it may be a different circumstance from the first example.)

Basically, I want to know if the AD is calculated at the start of a cast, at the end of a cast, or when the ability actually creates and object on the battlefield.

As long as the spell hasnt shot yet, like to use your example Caitlyn's ultimate. if shes aiming her shot and hasnt shot the bullet, you can apply the extra damage as long as you can do it before the hits the enemy. As the damage isnt applied until the target is hit, any buffs or anything like that calculate when the champion is hit as opposed to when you start casting a spell. Thats what makes sense to me.