Your phrasing is fine
For comparison, look at Counterspell, it has a reaction timing identical to the reaction timing you list, differing only in range:
when you see a creature within 60 feet of you casting a spell
Counterspell interrupts a spell--happening before the spell goes off. Now, why is this? Well...gotta rummage deeper into the English language a bit. The rule for Reactions as specified in the DMG (page 252) says:
If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action.
But in this case, the timing is being specified by the word choice. Specifically, the tense being used and the fact that the trigger is you seeing something. If you look at most Reactions, the language used is in the Present Indicative. "Makes a Save" "Takes Damage" "Dies" "Succeeds on an Attack Roll or Saving Throw."
Present Indicative is used to refer to something that has occurred in the general present time frame, but is not appropriately used of something actively happening right now. For comparison, Counterspell uses the word "Casting" which is in the Present Progressive, which is used to specify things that are actively happening right now.
So, Counterspell's timing is specified by the phrasing used. Reactions occur after their trigger, and the trigger is when you see a spell being cast, not when the spell is finished casting, as would be the case if Counterspell said "When a creature you can see casts a spell."
Can we make it better?
If you want to avoid any confusion and not have to get this deep in the weeds in the English Language, I suggest just copying the second half of the Reaction Timing from the spell Temporal Shunt which says (emphasis mine):
taken when a creature you can see makes an attack roll or starts to cast a spell
It's basically saying the same exact thing, but in plainer terms.
A Brief Warning
As-written, this Reaction would allow your monster to dodge many spells, not just Forcecage, assuming the environment is amenable to it.
Depending on the creature's speed, they could either run away from where they're standing to try and get out of an AoE, or duck off to somewhere with Total Cover and render themselves invalid targets to a targeted spell (or out of the AoE of a spell that doesn't spread around corners).