Does this conflict between Asgardians and the Tuathains occur openly in the Destiny Cycle Series?

Not initially, as the first two books, Blades and Stone of Destiny, are more focused on the physical nature of invaders-turned-settlers (aka Norvegrs – as the Norse called themselves in the 5th century) and the defenders of the Emerald Isle (aka the Gaels). The hostility is not evident between the two sets of gods until Heart of Destiny.