Does "when move" trigger and resolve before any showdown happened?

Yes, "When I move" triggers resolve completely before a showdown (combat) begins.

According to RiftJudge FAQ #10571 and Rule 441.3, the sequence is as follows:

1. Movement: A unit moves to a battlefield. Moving is instantaneous and does not use the chain (Rule 441.3).
2. Triggered Ability: "When I move" triggers are placed on the chain.
3. Reaction: Players may respond to these triggers while they are on the chain.
4. Resolution: The chain resolves (LIFO). Because a showdown can only begin when there is no existing chain (Rule 340), the "When I move" chain must be completely empty and resolved before the showdown can officially start.
5. Showdown Begins: Once the "When I move" chain is resolved, the showdown begins, and "When I attack" or "When I defend" triggers are then placed on the initial showdown chain.

In summary, a showdown cannot start while a "When I move" trigger is on the chain. The trigger must finish resolving first, clearing the chain, which then allows the showdown to begin.