Those PvP islands have some technical issues still.
One is that when you send reinforcements and the island is captured or attacked by another captain while the reinforcements are travelling, they dissapear. No idea where they are going. Not going to the island, not returning to the base.
Another is that they do not have the little arrow showing their direction on the map like the home haven and target islands have.
Also the battle reports do not come or come with big delay. I had one report about it been captured. And long after I got reports about 2 attacks that had been before the final attack.
For more: There is delays with the map. The island have been taken from you still shows that you have it. So you can not resend capture to it from the map, you must go to the lighthouse. It enables the sending of reinforcements on the map though, but do not where those would go when you do not hold the island.
So conclusion the basic functionality works for PvP. But otherwise it is a mess.