I live in New York. I Prayed in a shul tonight and they said Sefirat Haomer with a Bracha after Maariv before Tzait Hakochavim (I believe its when three stars are visible). I thought that one must wait until after Tzait HaChochavim to count Sefira along with the saying of all three parshiot of Shema. Can one be Yotzei Sefira and Shema even before Tzait HaChochavim arrives or do I have to repeat it later on in the night? this shul confused me very much.

Firstly, you should check local timetables for times of Tzait Hakochavim to verify if the sefira was indeed counted before the proper time. You are right that to begin with one should count only after Tzait Hakochavim .But, the Mishna Brura (תפט: טו) says that according to some opinions if one has counted during "Ben Hashmashot" he fulfilled the mitzvah. However, the Mishna Brura brings another opinion that if one counted during Ben Hashmashot he should count again after Tzait Hakochavim without a bracha.