Note: I agree with most of this fine answer, but sometimes it's useful to have other voices address the same topic in a different way.
Immediate actions typically don't interrupt other actions
The flowing monk archetype's extraordinary ability redirection says that "as an immediate action, a flowing monk can attempt a reposition or trip combat maneuver against a creature that the flowing monk threatens and that attacks him," but it's only upon a creature actually making an attack roll that a creature knows it's being attacked, and making an attack roll means either the attack hits and delivers its effect (typically lethal hit point damage) or the attack misses.
In other words, the foe attacks the flowing monk and either hits and delivers its effect or misses. Then the flowing monk can take an immediate action to use the ability redirection.
This, I think, addresses the entirety of the question's timing concerns. Since the immediate action happens after the attack's resolved, the effects of the immediate action aren't occurring while the other actions remain unresolved.
"You gotta be kidding! That's terrible!"
An attack roll represents an "attempt to strike your opponent on your turn in a round. When you make an attack roll, you roll a d20 and add your attack bonus.… If your result equals or beats the target’s Armor Class, you hit and deal damage." That happens all at once. So, unlike in certain trading card games, for instance, before a creature makes an attack roll, a creature isn't committed to any course of action, and after a creature makes an attack roll, the attack either hits and delivers its effect or misses.
So unless an effect specifically says otherwise—and the flowing monk archetype's extraordinary ability redirection does not say otherwise—even an immediate action cannot be taken after the creature declares an attack yet has not made the attack roll (because there is no declare phase in Pathfinder) nor can an immediate action be taken after an attack roll yet before the result is determined because determining the result is part of the attack roll! (That is, simply making an attack roll means either the foe suffers the effects of the attack or the attack misses; making an attack roll does not mean that an attack is, like, on the way! O, no! I better do something!)
For the flowing monk archetype's extraordinary ability redirection to have the possibility of foiling the attack, the redirection ability must, for example, say instead As an immediate action, before the foe's attack roll result is revealed a flowing monk can attempt a reposition or trip combat maneuver against a creature that the flowing monk threatens and that attacks him. I'm not, like, fabricating this before the result is revealed language because I have a hidden agenda and secretly hate immediate actions or anything; that kind of language is used throughout the game.
Also, although an immediate action "can be performed at any time," the immediate action description does not say that it can be taken so that an immediate action can interrupt other actions. Contrast this with, for example, the ready action action, which explicitly says that it can be taken so as to interrupt some actions. The typical immediate action is still taken in sequence after another action resolves and not while another action remains unresolved.1,2
This is a good thing! Honest!
The hardest part of role-playing game design is configuring the system's action sequence. Pathfinder (like its forebear D&D 3.5) tries really hard to avoid significant actions taking place during other actions because, as the question's example illustrates, this raises all sorts of impossibly messy questions, leads to sleepless nights on the parts of GMs, and makes players rage-quit over their GMs' rulings.
Further, were the game to allow actions to be taken consistently while other actions remain unresolved—that is, actually interrupting those actions—, everyone must be given the same opportunity to interrupt each of those in-progress actions during those actions' discrete steps. That's incredibly tedious, and the game often doesn't provide a clear indication of what those steps even are!3
So does this inhibit the combat efficacy of the flowing monk archetype's extraordinary ability redirection? Some. I mean, sure, a flowing monk will probably want an even higher AC than he previously wanted, but, in exchange, it means combats are not like this:
GM: The orc is going to attack the flowing monk.
Player: I'm going to take an immediate action to use the extraordinary ability redirection against the orc. I take an immediate action to use the extraordinary ability redirection. I'm going to make a combat maneuver check against the orc to trip the orc. I make a combat maneuver check against the orc to trip the orc. I'm going to tally my result. I tally my result. I'm going to reveal my result. My result is 19.
GM: I'm going to reveal the result of your trip combat maneuver. It is successful. You will have tripped the orc, and the orc will end up prone in its square.
Player: I'm going to make an attack of opportunity against the orc because I successfully tripped him and I have the feat Great Trip. I make that attack of opportunity. I'm going to make an attack roll. I make an attack roll. I'm going to tally the result. I tally the result. I'm going to announce my result. My result is 17.
GM: You're going to hit and deal damage to the orc. You hit and deal damage to the orc.
Player: I'm going to roll damage for my attack. I roll damage for my attack. I'm going to tally my damage for the attack. I tally the damage. I'm going to reveal how much damage I dealt. I dealt 7 points of damage.
GM: The orc, having been tripped, falls prone in its square. The orc makes an attack roll to stab the flowing monk. I'm going to tally the result. I tally the result. I'm going to announce the result. The result is 15.
Player: My flowing monk's AC is 14.
GM: I'm going to roll damage. I roll damage. I'm going to tally damage. I tally damage. I'm going to announce the amount of damage dealt. The orc deals the flowing monk 5 points of damage.
…Because nobody wants to play that game! (That's an exaggeration, of course. I am certain some folks do want to play that game, but—and I'm gonna go out on a limb here—I think the vast majority prefer to leave such complex event chains to, for example, trading card games.) Also, note that issues can be taken with the above example: I had to guess at some steps in the different events because sometimes the game doesn't make it clear what the steps exist as sometimes there aren't supposed to be steps. That is, even determining some steps becomes an exercise for the GM! Yuck. Seriously, in all but the rarest of cases, leaving taking actions—the absolutely most crucial part of any role-playing game4—in the hands of the GM rather than to the rules is, frankly, a recipe for shouting matches, broken friendships, and reality-checking the GM's rulings via real-life brawls.
So, rather than combat following the example process above, combat goes like this:
GM: The orc attacks the flowing monk, getting a result of 19 on the attack roll.
Player: My flowing monk's AC is 14.
GM: The orc hits and deals 5 points of damage.
Player: I take an immediate action to use the extraordinary ability redirection to make a trip combat maneuver check against the orc, getting a result of 19.
GM: The orc falls prone in its square.
Player: Because of my Greater Trip feat I make an attack of opportunity against the orc, getting a result of 17.
GM: That meets or exceeds the orc's AC.
Player: I rolled 7 points of damage.
GM: Okay. The orc's prone and wounded, and you're less wounded. Who's next?
And this, by comparison, is clean, neat, fast, and playable. It does sacrifice on that altar of playability some of what might be seen as the cinematic nature of the flowing monk's redirection ability, but that's a relatively small sacrifice in light of the alternative.
1 To be silly about the ability to take immediate actions at any time for a sec, an immediate action also can't be taken five minutes from now, five minutes ago, or during the Cretaceous period (unless the creature's, like, in the Cretaceous period right now, of course). I mean, really, either at any time means literally at any time or it doesn't, right?
2 This is also why an action readied via the ready action typically—interrupting a spell being cast being the prime exception—is taken and resolved first, before the triggering event. Confusion avoided! That is, unless the GM allows creatures to pick ready action triggers like While I'm being stabbed or If I'm falling down a 10-ft.-deep pit. So don't do that.
3 This answer deliberately ignore players actually and in real-life interrupting other players to say what actions their PCs will take. I am unaware of a role-playing game where a player is supposed to yell I stab him! while another player's talking is codified as the preferred method of managing the game's action economy. I suspect there's probably some RPG that uses such a system, though.
4 That, however, is not an exaggeration. RPG Design Challenge: Design an RPG that's both fun and in which PCs don't take actions. Renaming actions, for example, moves doesn't count. (O, and it also doesn't count if the RPG has PCs that cause others to take actions nor if the PCs take actions in the Matrix or in a dream or whatever so that the PCs are not really taking actions. Nice try.)