I have added the lsPage.context.setDomain() on the engine configuration, and the push page is able to open with firefox now but I am not sure whether I miss something or what, the lsPage.context.setDomain() seems doesn't work on IE browser and prompt me the following message while connecting:

1: 17:43:21,255 ER bind Unable to find the Engine. Retrying. If the problem persists, please check your configuration.

Therefore I have added the browser detection in the script and call the seDomain method accordingly. Both IE and firefox are working now.