Scrap Field

It happens for the player who claims it, whoever launched it. A claim happens in the battle step of its claimer's own turn (706.3a), so it waits for that turn's second watch, and happens as it starts (706.6a). You keep this steam until the end of the phase; it pays your costs first. What you don't spend by then is lost.

Crew dispatched here on their own turn make progress, whoever launched it; on the opponent's turn they can only fight (706.3a). The first player to reach 2 progress claims it and gains 1 spoils.