I had this issue a few months ago and, being that I was new to the city, had never dealt with this, and had a lot of misconceptions about the pests, I know how nerve-racking this can feel.

Fortunately, my super got this taken care of quickly and I will tell you that the biggest red flag for me is that the exterminator didn't come back for three weeks. There should be at least three treatments about one consecutive week apart to be effective, and more if they've really taken hold. That's what happened with my building's situation as well as the situation at my office.

I will also say that while you can bring them in on your own quite easily, especially in a city like New York where they are easily spread, based on what your neighbors say, it could just as well be the case that they were already in the building and as a previous commenter said, they do spread between apartments on their own.

Also, you super is legally required to take care of the issue within thirty days if I'm not mistaken.