Question for the grammar Nazis

[Ghoulish Delight]

There's no "right" answer in this case. You can't really go on the plural thing because, while the word "Productions" is plural, the entity as a whole (which is the possessive subject) is a single company. So it's one of the few instances where "Whatever sounds better" wins. Since "Productions's" would be pretty awkward to pronounce, "Productions'" is probably the better choice.