The Confederacy has also had jurisdiction over the Ruby Sea for as long as everyone in Doma and Hingashi can remember. If Hingashi really wanted the Confederates out of the Ruby Sea, they would have forced them out long ago. The only reason why Hingashi has refused to play ball with the Confederates in recent times is because Yotsuyu declared them to be unlawful under Garlean rule. The Hingans decided that was fine since that meant they didn't have to pay the Ruby Tithe which they'd been paying for as long as they could remember.
Incidentally, the East Aldenard Trading Company isn't complaining about the Confederates' tithe; they're just happy to be able to do business with them since the Confederates have stuff the EATC wants at reasonable prices. Ironically the people who are buying Confederate goods from the EATC is Hingashi, who the Conferates used to do a lot of business with. Ever since the Confederates were banned from coming to Kugane there's been a shortage of goods from the Ruby Sea in Kugane itself.
Provided they weren't bothering the Eorzeans, the Eorzeans probably wouldn't do anything. As it is, this is already happening somewhat, only it's not with Hingashi, it's with the remains of the XIVth Legion. Castrum Marinum is portrayed as being somewhere near The Cieldalaes, a group of islands in the Rhotano Sea halfway between Limsa Lominsa and Ul'dah. It'd be pretty hard to find a better place to threaten Eorzean shipping lanes. If the other Castrums are anything to go by, Eorzea isn't doing anything about them provided they don't start anything either (yes, I know the time-bubble is a thing, but considering Balasaur's Wall is still manned after all this time... yeah...). So Castrum Marinum is most likely still there. And if the Eorzeans are so busy they aren't bothering with the XIVth Legion, I have a really hard time seeing them bothering with anyone else.
Besides, that sounds like it'd be something right up Limsa's alley to look into. And Limsa only really cares about stuff like that if traders don't stick to the code. So long as they are legitimatize traders and not smugglers, I don't see anyone having a problem if Hingashi pulled something like that.