Each person handles stress differently. Most of the time it won't be stressful. You'll handle stress better as you gain more experience and understand how to handle various situations.
Most towers are a one-man operation such as Lead, Queens, Nassau, Brook, West Side Yard, Babylon West, and Babylon East.
Babylon Tower is shared between the East and West operators, so you aren't truly by yourself.
West Side Yard and Brook have a yardmaster.
The railroad is looking to centralize their operations so many of the towers are being integrated into the JCC Theater.
Queens tower has moved already and in the coming months Nassau will also be there.
The job becomes monotonous after a while.
After you become qualified, you can find other things to do while working (only if you're confident enough to not mess up).
It's basically a desk job that involves looking at train routes/timing on screens or a model board, deciphering that information, and making decisions via mouse click(s).