No, who mass produces the beverage, not the container.
All large soft drink companies either own or have relationships with local or regional 'bottlers'. The term bottler dates back from when all drinks were produced in reusable glass bottles, not from the fact that they manufacture bottles.
These days local bottlers make, sell and deliver all manner of carbonated and non-carbonated drinks as well as owning the sole rights to produce and distribute in their area. So while the formulas to make Butterbeer and Pumpkin Juice may have been created at Universal, it would not make sense to produce them there (though I'm sure UO retains all rights of manufacture). A local bottler, most likely the local Coke bottler, would be able to produce the products to any spec for much less than anyone else as they have the manufacturing and bottling operations already in place. Bottling production lines are quite large.