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In D&D 5e, movement and actions do not consume time, they consume actions. The game is inherently turn based. Actions happen in sequence, with each happening completely before the next can begin. The one exception is Readied Actions, which may interrupt other actions during a turn.

In D&D 5e, movement and actions do not consume time, they consume actions. The game is inherently turn based. Actions happen in sequence, usually each action completes before another can begin, the exceptions are movement (which can be broken up between actions or attacks on your turn), Bonus Actions (which can occur between attacks on your turn) and finally Readied Actions. Readied Actions use your reaction to allow you to act in response to a trigger, which may interrupt other actions during a turn.

The Ready Action lets you perform an act in response to a trigger using your Reaction. This act can be anything you could have done on your turn with your Action, in this case the Owl is readying the Dash action.

The Ready Action lets you perform an act in response to a trigger using your Reaction. This act can be anything you could have done on your turn with your Action, in this case the Owl is readying movement.

When you trigger then Owl's movement, it instantly responses by taking the Dash action and moves to the desired position. Then you "continue [your] turn right after the reaction".

While your attempts to make this logical and account for realistic movement are admirable, they do not align with the actual rules of combat and action resolution.

When you trigger then Owl's movement, it instantly responds by moving to the desired position. Then you "continue [your] turn right after the reaction".

While your attempts to make this logical and account for realistic movement are admirable, they do not align with the actual rules of combat and action resolution. Rounds, Turns and Actions are an abstraction of game-time passing. A round is approximately 6 seconds but turns do not resolve in real-time. Their resolve mechanically in initiative order, which follows the sequence I have laid out above.