In addition to the production method you describe, there are biotechnical ways to manufacture these, some of them vegetarian/vegan, some not.
If they are made by the described method from fish, they are definitely unsuitable to be called a vegetarian food, and the same applies to any food these have been intentionally added to.
If made from fish only, they and the food containing them could still perfectly be called a pescetarian food.
If the food isn't labelled as suitable/unsuitable for vegetarians, only the manufacturer can tell you who makes the additives they use, and how they are made. Unless somebody asked them already and put the answer online. Some manufacturers will refuse to disclose what they source, OR will refer you to the manufacturer of their additives, OR will tell you they are using product XY now but will not guarantee that they will not use another product manufactured in a different way in the future.