Season names only work for three-month (or six-month) turns (imho). Please consider just using the month names instead.
Consider this. Assuming you're using a northern hemisphere calendar year (ie. not a December to November year), winter is the first two and last month of the year. So winter is both before and after every other season in every year. If you had ten- or eleven-month turns, you could have two that were winter of the same year - Winter 2013 (Feb) followed by Winter 2013 (Dec).
I've looked at that code and I'm not certain how the game assigns which method is used. AIAndy rewrote that section a year or so ago so if he can fix that soon then that would be nice.