I used to dread this phrase. It seems like it's just clarifyins the timing of an interaction, but in reality, it's introducing an awkward pause into the flow of my combats. If nobody has any abilities like this, an attack goes quickly - they announce the attack and roll for it (understanding that the roll is void if I disagree about their attack), then announce the total, and I tell them what happens. But as soon as anybody has the option to intercede somehow, every such interaction gains an extra step (or several), while I prompt each such player to see if they want to boost the roll before I tell them if it succeeds. Worse, those players all then have to keep track of what rolls have hit and missed each type of creature, so they can use their abilities effectively.
I've decided (as usual) that my convenience is more important than keeping my players in the dark. For some time now, I have just replied to each attack (or save, etc) by telling them how much they missed by. That makes it easy for players to know the exact AC of their enemies, and shortens that pause significantly - now I tell them "you missed by 1", and immediately explain how close a shave it was. I allow players to interrupt me and apply their intercession up until I have to roll more dice or reveal previously unknow information or abilities (or until the next turn starts); I find that rolling back what has happened that far doesn't really hurt the flow at all. Example:
Me: The dragon breathes its Breath of Unpleasant Odors upon you. Me: Ok, give me a Dex save, Fitar Fitar the Fighter: (roll) 12 Me: That's 3 shy - the odor is intense, and your character now smells terri Fitar: Wait! I'm going to add my inspiration die! Fitar: (roll) Ugh, a 1. Me: ... now smells terrible, and Wyzad the Diviner: Hold on there, I think he actually rolled a 15. That man never showers. Me: Thinking quickly, Wyzad protects his nose in the only manner that occurs to him, averting this smelly vision of the future. The Unpleasant Odors stream past you, relieving your poor DM of the need to dig out a thesaurus for synonyms of 'smelly'. Me: Honestly though, prestidigitation would have worked fine.
It's a minor boost to the effectiveness of such powers, but it saves me time, and them mental effort. I generally compensate for this (and all the other nice things I give them) by adding monsters and HP to most encounters - the hardcover encounters aren't really designed for parties full of optimizers anyway.