Unless people are getting paid off to look the other way?
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.
"The military of Country X is firing on and sinking our country's vessels" is much more likely to lead to retaliation. China may not have the navy or willingness to project power across the Pacific, but I guarantee they have the capability if focused to utterly destroy the computing infrastructure of the country - and while enthusiastic private parties may not get involved in civil penalties, "Argentina just declared war on us!" is a hell of a rallying cry.
Edit: also keep in mind that even governments are not monolithic entities with a single mind. Those costs are coming out of someone's budget.
Of course you gotta cut a lot of economic ties before you start poking pooh bear.
This sounds a lot more like "selling back".
Which makes a lot of sense if you don't have anything better to do with it... just make sure you're selling it back for enough money to make a good profit.