I would suggest perhaps integrating the government types gradually if you are trying to play historically. In most of Great Britain, the province should start as a Type III (Client Tribe), representing that early on, the King will not directly control the province, but instead control it indirectly through an appointed local noble. Then the transition could occur towards the Type I government, first by using clerical administration (Type II) and finally coming directly under the King's control with a Type I. This is expensive and takes a long time, but it could better represent just how long it takes to integrate a province fully. Again, this is mainly guesswork, because I don't know a huge amount about how the Casse would have administered outlying regions, so I may be wrong. I think that in Ireland, and maybe even in Caledonia (Scotland), you might want to use a Type IV if you're playing historically, to represent the difficulty the Casse king would have in directly controlling culturally different peoples that were far away from the capital in the south of the isle. Since the Casse are a Belgae tribe, I think building a Type I in the two Belgae territories would make sense, due to the level of cultural similarity, but you may want to use the same gradual process as stated above. Again, just a guess on my part.
Couldn't have said it better myself. I like a slow gradual process for bringing new provinces into my faction.