How can you consider a card has been played? I am confused because a lot of cards say "when you play me" then the ability of that card will trigger.

A card is considered "played" (for trigger purposes) only when it has finished resolving — not when it's put on the chain (Rule 419.4.a). So "When you play me" fires after the unit is already on the board: you play it → it finalizes and enters play instantly → only then does its play trigger go on the chain as a separate reactable trigger (Rule 383.4.a.2).

That's why the wording exists: the trigger happens immediately after the card resolves, and the unit is already a game object when it does. This also means opponents can't react to the unit entering play itself, but they can react to the play trigger — and if they kill or recall the unit in response, the trigger still resolves (it just may do nothing if it references "me" or "here").

One caveat: "play" has three meanings in Riftbound. As a trigger condition it means "resolve," but when an effect instructs you to play a card it means "put it on the chain and finalize it," and static cost-checks like Battering Ram count cards as "played" once they're finalized. The "When you play me" template is always the resolve version.