Game-theoretically, it seems preferable to sink them without any warning.
Consider: the fines would only be paid if they are less than the cost of acquiring a new ship. So if they have to pay fines of 90% of the value, you're still saving them 10% compared to getting a new ship. And if the fines are >100%, they would just ignore it and leave Argentina with the ship.
Unless Argentina can turn it into a revenue stream, sinking them unconditionally seems preferable. The Chinese fishing boats don't have anything to give them in a negotiation. All they have to give them is leaving the area, and that is accomplished by sinking the boats too.