background.js

//you cannot use the chrome.windows api in the devtools.js page.
chrome.windows.onFocusChanged.addListener(function (windowId) {
    //send message to devtool.js. Then you can re-evaluate ko.dataFor($0)
    chrome.tabs.getSelected(null, function (tab) {
        chrome.tabs.sendMessage(tab.id, {}, function (response) {
        });
    });
});

// notify of page refreshes
chrome.extension.onConnect.addListener(function (port) {
    port.onMessage.addListener(function (msg) {
        if (msg.action === 'register') {
            var respond = function (tabId, changeInfo, tab) {
                if (tabId !== msg.inspectedTabId) {
                    return;
                }
                port.postMessage('refresh');
            };

            chrome.tabs.onUpdated.addListener(respond);
            port.onDisconnect.addListener(function () {
                chrome.tabs.onUpdated.removeListener(respond);
            });
        }
    });
});