I tend to overemphasize the existence of turns and rounds.
I use turns for more than just combat, I use them for the Explor/Roleplay portions too. If the characters walk into a town I go around the table and let each player pick one thing that their character is going to do in town. They declare the intention, and I ask the remaining players if anyone would like to go with them. Let's say the Cleric went first, and said she wanted to go to the shrine. The Paladin and the Fighter want to go with her. Next up around the table is the Bard. When I ask him what he wants to do I say "What would you like to do while the three of them are at the Temple. Obviously, it's easier to do this out of combat, but in combat I have already had to say things like "at this point in your turn, I don't think he had made it that far yet. If your action depends on his (concurrent) turn having finished, then you have to ready that action instead. Don't worry, it will trigger when this round is over."
To put this in railgun terms; When railgun sprite #3 takes it's turn, I'd say that the object being passed is still making it's way from railgun sprite #1 to railgun sprite #2. the sprite could ready it's action, but you are going to see that object behave exactly as it would in the real world. In the first round, sprite #1 passes the object, sprites 2-200 ready an action. next round, sprite #2 passes the object, sprites 3-200 ready an action...
When the rules (yes, even as written) allow for stuff like this, anyone who really thinks a DM should allow it is playing this game for different reasons than I. Anyone who doesn't feel like they have the right to correct it in their game? You don't; you have the responsibility to correct it. It is asinine to argue against a DM who wants his world to make sense at the expense of your "trick".
As it relates to the thread; The player moves on his turn, while the owl readies an action (fly as soon as his movement is up). The owl effectively loses it's action this round, but as soon as the round is over the Owl's action is triggered and it takes it's movement before the first (initiative) turn of the next round takes place. The question is, would the owl get to take a turn in round 2? I'd say yes, seeing as how the player already compromised, but that could be another thread altogether...
The rules are like the strands of the weave, they must be coaxed and manipulated in order to achieve the desired result. If you want a world with railguns and twin-immovable-rod-wielding bag-of-holding-exploding nonsense, you can use the rules to make that happen. If you want a world where things... fall when you drop them... there are interpretations of the rules for that, too.
dang, I might make that last paragraph my signature quote...