It seems bizarre, doesn't it? Two adversaries represent two opposing clients who are actually pleasant and respectful of each other? It doesn't make sense. It's not what you would expect.
The reality is that in New York lawyers are obligated to treat their adversaries with respect. Lawyers are charged with being polite to opposing counsel. In fact, this has been required by the office of Court administration which governs all lawyers in the state of New York.
Years ago there was no such requirement and often times lawyers got into a verbal brawls and huge confrontations over the most ridiculous things in a lawsuit. One lawyer would show off for a client for no other reason other than to create a show. Others had truly hard feelings toward their adversary and never wanted to give an inch with the most inane requests.
When you go for your question and answer session, known as a deposition, you might be shocked to see the attorneys being polite to each other prior to the start of your questioning. You might be surprised to hear them talking pleasantly to each other during a break. Rest assured, this aura of politeness does not change the fact that each attorney still vigorously represents their clients.