I'm pretty sure it updates when you happen to visit the island. There is no support for having it go look for itself.
Most of our Big Island support is in webui/IslandDecorator. We also have IslandArenaRequest to attend concerts, PyroRequest to visit the lighthouse, and the "nunnery" command submits a raw GenericRequest to visit the nuns. Breakfast (during the war) will visit the farmer to collect his reward, using a GenericRequest.
I wonder if all this can be rationalized so that IslandRequest, say will visit either bigisland or postwarisland, as appropriate, and will handle logging requests and parsing responses that go to those places. IslandManager might keep track of the internal state, and IslandDecorator would do just the Relay Browser decoration.
We could have IslandRequest() - no arguments - be a "visit the current island" request, the result of which would update state based on what it sees on the map.
Regardless of code cleanup, the issue remains that the variable result from the claymore will make accurate trapping of war kills impossible. If you are looking for a Wossname, say, you are out of luck. And do we really want to automatically submit a request to look at the map after you use a claymore? We'd be better off filing a bug report with KoL, asking that the result of the item use actually tell us how many combatants were blown up - even if only in an HTML comment, in case listing the actual number visibly is deemed to be "not funny".
As if war is "funny".