Why is the Rosh Hashanah for trees in Shevat? Why is the season of blossoming the determining factor for setting that date?

Why do Beis Hillel set the date of the Rosh Hashanah for trees on 15 Shevat - the middle of a month? What is behind this disagreement between Beis Hillel and Beis Shamai?

Since this date for the new year is based on winter rainfall, what should be done with fruit from the southern hemisphere - where Shevat is in the summer? (For example, grapes from South Africa were imported and processed into wine in Eretz Yisrael, obligating them in Ma'aser.)