First off, just to add more clarity, there is no worldwide patent, that is a patent that can be enforced all over the world. Some countries might not have IP rights as such.
I assume that the 12 countries where the product is deployed have a patent system. Generally huge MNCs would prefer for filing patents all across the world, since they have the resources. If a smaller company is to file for patents, then it would think about the size of the market in the country for its product(s). Once decision on the best possible successful market is made, it can file a patent in that country and later use this filing date as priority date in other countries subsequently where ever it is filing for patents.
It should be noted that patents can be used in two ways (i) to prevent someone from infringing your patent by manufacturing/making/selling the patented product and (ii) to prevent someone from importing the patented product into the market. So the company has to think about these aspects as well, in terms of its capacity to make a product locally in a market or export the final product to another market where the company has patent protection for its products.
Moreover filing in all countries may not necessarily be useful, and in some cases the patent fee will just be an expense.
So essentially the answer is it depends on the IP strategy which the company wants to work out. Hope that was useful.