There is no "should" or "shouldn't " per se. It is all negotiable and part of the overall deal. We purchased in May with all 2016 and some banked 2015 points, and the seller paid the 2016 MFs because that was our offer.
However as PP mentioned, 2016 MFs should have been paid January 2016. You would actually reimburse the seller if you were to pay 2016 MFs.
Edit: Most usually will say that the buyer should pay 2016 MFs if the 2016 points are intact, however I have heard the argument that because Disney charges MFs based on calendar year, then in theory the buyer should pay MFs by calendar year. The reasoning behind this is that when you buy a contract directly from Disney, your MFs are prorated based on calendar year. If you were to buy a contract right now, whether you bought a February UY or a December UY, your MFs would be exactly the same. MFs are prorated based on remaining months in calendar year 2016, so you would pay about 2/12ths of it. However, the Dec UY would get all 2015 AND 2016 points, while the Feb UY would only get 2016 points. So you can see Disney charges MFs independently of the actual points you get.
I don't know which is "correct ", although ultimately as I said I don't know that it matters. Everything gets converted to a $ lump sum at the end.