To interrupt another character's turn usually takes a Reaction
The problem here is that the game's mechanical means to interrupt another's turn is the reaction. Dropping concentration does not require an action (and since action and reaction are similar currency, should not require a reaction) so you need to discuss with your DM whether or not you can (1) by default interrupt any currently declared action/event to stop concentrating at any given time, or (2) if you must wait to stop it when it is your turn.
- For case 2, if as the flying creature approaches you he sees you dropping, would he not adjust his course to try intercept you?
And for case 1, how does the DM determine if he got off that shot before you stopped concentrating? Dex check? Int check? An advocate for that character could argue that they loosed the shot "at the apex" before they you noticed them and chose to stop concentration.
It might seem to a given DM that you are manipulating the turn system mechanics to provide a mini-time stop that allows you to interrupt their turn. Discuss with your DM. The only mechanical means to an instant response (reaction) seems not to fit this situation.
Certain special abilities, spells, and situations allow you to take a
special action called a reaction. A reaction is an instant response to
a trigger of some kind, which can occur on your turn or on someone
else’s. (Basic Rules, p. 73)
Since neither of those spells explicitly has that provision, nor does the text on concentration, to interrupt another's turn then this requires a DM ruling in terms of timing.
Arguments for the interruption
Since your concentration can be broken on another character's turn (when damage is done to you) you can reasonably argue that dropping concentration on another's turn is consistent with that, since
You can end concentration at any time (no action required).
Lino's answer is a valid ruling, as would be a ruling that requires that you only act on your turn unless you have a mechanic that allows you to interrupt
another character's turn. Dropping concentration then (only on your turn) would not consume your action - you would still take an action of some sort - but you'd need to wait until your turn to declare that you are dropping concentration.
During a round, each character has a turn.
The game organizes the chaos of combat into a cycle of rounds and turns. A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative. Once everyone has taken a turn, the fight continues to the next round if neither side has defeated the other. (Basic Rules, p. 72)
OK, when it is someone else's turn ... what happens?
On your turn, you can move a distance up to your speed and take one action. You decide whether to move first or take your action first. Your speed—sometimes called your walking speed—is noted on your character sheet. The most common actions you can take are described in the “Actions in Combat” section later in this chapter. Many class features and other abilities provide additional options for your action.
Since the text on concentration does not require an action (small a) to drop concentration, nor a reaction, then parsing that text literally supports Lino's answer: you aren't using an action, so "any time" can be interpreted as "any time, to include when some other character is taking an action within that six second round."
But it's all "happening at once" during a round
A DM can also rule that you only get to declare what you are doing when it is your turn. Interrupting others (even NPCs and monsters) on their turn is not consistent with this being a turn-based game. Waiting for your turn is consistent with D&D 5e being a turn-based game, with the exception - reaction, which this is not required to use - being when you can interrupt another character's turn.
How often will you be happy to see the Monsters interrupt your turn?
When playing a turn-based game, how often do you want others to
interrupt you during your turn? And for that matter if, as the flying
creature approaches you he and sees you dropping, would he not adjust his
course to try intercept you? It doesn't take an action for him to see your location begin to change, does it?
Discuss this with your DM and get a ruling. Hopefully, for your idea to work, the GM will see it Lino's way. If not, then wait for your turn and do/declare stuff then.