Time is a fundamental element in Jewish life. Time reigns the whole dynamics of how to follow the Torah. As Shlomo HaMelech brings in Mishlei, there is a specific time for everything. Sefirat HaOmer is no exception to the rule. The Sefira should be said first thing on the day. Remember that according to Judaism, the day starts at night. The common custom is to say Sefirat HaOmer after the prayer of Arvit. As the majority of the halacha, there are different opinions and customs on how to follow the rule. 

According to Kabbalah there is a great benefit to say the Sefirat HaOmer at the earliest time possible. For instance, the Rashash advises the people who live outside Eretz Israel, that they have a second Pesach Seder. He tells them not to wait till the second seder is over to count the Omer; therefore, the chitzonim won’t have time to get strength. Rabbi Avichai is very meticulous to say Sedirat HaOmer at the earliest time possible. The more a person delays the Sefirat HaOmer the more negative influence he would have from the chitzonim. 

In Judaism there are two halachic times that define the end of one day and the beginning of the next day. Shekia and Tzet Hakochabim. Shekia refers to the sun set where there is still light of the day but the sun is already gone. Tzet HaKochabim...