Living in NJ, working in NYC

I worked in NJ until April, and my work transferred me to NYC office since then. I tried freetaxusa today to see how much I owe/get refund (tried turbotax as well but one of category was not acceptable while entering W2 info, so no luck). I have 1 W2, very small amount of 1099div and 1099int. It's the first time for me to file 2 states taxes. I answered all the questions like how many days you took vacation, sick leave, work days outside of NY, etc for NY filing. Fed and NJ refund is very very small, but I owe $1000+ for NY. It doesn't seem right... or maybe I did something wrong. Withholding 0 as single, filing as married filing separately, no kids, no homeowner. My tax filing was very simeple until I transferred to NYC office :( I am going to contact an accountant next week, but just wanted to hear your experience if any similar.