Probably not the best idea to interject between two people talking past each other, but . . .
Nothing in either of those sentences (as I'm reading it; and as I (basically) understand angularjs) implies (to me) that the client triggers anything. The flow of information (after the websocket connection back is established) for the purposes of display is all server => client.
The client opens a ws connection back to the server and then sits and waits (passively, patiently) for events to come in on it. When a value changes on the server the server sends an event to the client side with the new value ("Hey you: foobniz is now 'vreemflitzle'!"). The client processes that event by updating its local cache of that value, updates anything in its virtual copy of the dom which is dependent on that value, and repaints anything in the real dom which has changed.
The cake is a lie.
The cake is a lie.
The cake is a lie.