Rules question about Pirate (action-reaction-duration)

[suet63]

My conspirator becomes terminal, it means it doesn't count as I 'play' Pirate this turn. So it has to be I played Pirate as 'reaction' in the previous turn, but I thought the duration effect means I play it this turn as well (to gain Collection)? Pirate is 'action' card, and the ability above the line is its action, I execute the effect this turn so it should mean I play the action part this turn?

photo : https://imgur.com/a/MklqD6m

[Ingix]

You played the 2 Pirates on your turn 13. What happened at that time is that each set up a triggered ability (to gain a Treasure), to be handled at the start of your turn 14. That's what happens on your turn 14. You didn't play the Pirate again that turn.

Setting up a triggered ability for a later turn is how most Duration cards work. They are played only when you put them on the table, what they do in later turns is not considered 'playing' them, as you correctly deduced from Conspirator being terminal.