Yeah, it doesn't make sense to make beverages somewhere else if you could make them near to the consumers, because almost all beverages are mostly just water, and water is heavy, so if you make it somewhere else you're also paying to move water for no reason.
The syrup is manufactured by Dr Pepper themselves (they couldn't keep the recipe secret otherwise, as Coke famously did). Sometimes the carbonated water is added and bottled by various distributors to be more specific. But there are also clearly economies of scale with bottling plant size, location, shipping costs, retail channel partnerships, jurisdictional regulations, etc that factor into where this bottling takes place.