I would think it's much more likely that a forcemaster came to the Anvil Throne mountains and taught the young dwarf. Digur is one dwarf. In an individual's life, all sorts of circumstances can happen that go against the norm. Just a thought.
I wonder why they let the foreigner in their territory and live there long enough to train Digur. I think it's more likely that they would have sent Digur away somewhere else to train, since they probably wouldn't invite a foreigner into their territory if they didn't have to. And also because he probably annoyed them in the same way Lithann annoyed her people.
Also, if they don't ever send any mages to train in other countries, they would be at a significant disadvantage both in the arena and in war, because other countries would have learned of a wide variety of tactics and how to counter them, and the Anvil throne would not. For an industrial nation of pragmatic dwarves whose territory is highly coveted by their enemies (and they probably have lots of enemies, considering how valuable harshforge is), that is unbelievably stupid.
The arraxian crown wants their harshforge. Westlock probably wants it to, and will try to get it before the arraxian crown can lay their demonic hands on it. Westlock is a much more powerful nation than the Anvil Throne. They might be apologetic about it, but they would still want to occupy the Anvil Throne to protect both its people and its resources from the forces of Infernia if they could do it in a way that they wouldn't lose favor in the international community. Regardless of whether the Anvil Throne wanted them there or not.
I'm guessing all it would have taken was for the anvil throne to start losing their war against the infernal invaders, and Westlock would have swooped in to "save" them. It's fortunate that the forces of infernia were weakened enough during the demon wars that the Anvil Throne could hold them off without Westlock's "help". Although if their Mage's aren't familiar with foreign battle tactics, then it's kind of hard to see how they could have won, at least not without massive casualties.