Dues are paid on a calendar year basis, not based on UY. The bills will be sent out at the end of December 2015 for calendar year 2016. If you opt to pay in full, the due date is Jan 15 but no late fees are assessed until after Feb 15. You can pay by credit card, check, debit card or gift card. Many people choose this option so that they can pay by credit card and get reward points.
You can also pay monthly. There is no fee to do this which makes sense to me because you are "paying as you go", giving Disney the money as it's needed to pay the bills. However with the monthly payment option they want your payment in cash and on time so you must pay via direct debit from a US bank account. You can choose between the 1st or the 15th of the month as your payment date but the initial (January) payment is always on the 15th. If the actual property tax due for the prior year ends up higher than the estimated taxes paid as part of the prior year's dues, the additional amount due is added to the January payment, making it higher than expected.