The explanation in Ohev Yisrael is: “On [the first of] Tishrei the thought came to His mind to create the world, as the paytan notes (in our Rosh Hashana liturgy), 'Hayom harat olam ? Today You have conceived the world.' However, the actual creation was in Nissan.”
He then goes on with a lengthy explanation, comparing the tree to the original Creation by presenting the month of Shevat as a microcosm of the 12 months of the year, and he divides Shevat into two parts.
The first half of the month, starting with Rosh Chodesh, is compared to the conception of the tree, the part of creation that is hidden. This is the essence of Beit Shammai's opinion, whose rulings hold sway in the Heavenly Court.
Beit Hillel, on the other hand, represents that which is revealed like the blossoming of the trees. For the most part, the blossoms appear on the first day of the second half of the month, the fifteenth day ? Tu-BiShevat.
In this, the revealed world, we usually follow Beit Hillel. That is another explanation for celebrating the New Year of the trees on the 15th of Shevat.