It's an interesting suggestion. After working in several concepts for EBII, I can say that I always try to get this type of immersion through three elements. As it has been pointed above, for me the historicity is the basis of this immersion but it should be combined with fresh concepts always related with the playability. Well, these three elements are:
-Traits and Ancillaries: it is the most interactive element. The player can learn history thanks to them but at the same time he has certain degree of control over them, so the historicity is combined with the roleplay and the player has the feeling of controlling certain aspects of the life of his family members. The other aspects have told by the game so he must accept them like in a roleplay. For example the revamped Arevaci/Celtiberians can be a good example: As you can see in twitter, you can decide to make a present in the form of a luxurious dagger, if you made that gift, the loyalty of your new friend will be increased and probably you will want to roleplay the new relation of friendship. At the same time there are other aspects that can be influenced by you but the degree of control is lower. For example, your family member can lost a friend or his hand after a hard battle via trait but if he emerges victorious, he could be the one who cuts the hand of an enemy or he could demonstrate that he follows the path of the Celtiberian warrior. If he visits a city he could get a pact of hospitality with another aristocrat and much more things. For example, if he goes to the south he could be recruited as a mercenary and he could fight for more than ten years!!! (you will lose the control of this FM while he is fighting as mercenary, after that he will return either victorious or defeated). For me this is the type of immersion I like for MTWII/EBII: most of your decisions will immerse you in X culture and the results will be fun. Additionally, they will be always at the service of both the history and the player.
-Uniques: As recent examples, that have been seen in twitter I can name the Punic settlement, the Lusitanian ritual sauna or the sanctuary of Ulaca. These type of buildings can't be destroyed and the player can imagine the world of his faction through several narrative texts and if he is interested on the institutions that are described, he can read the historical descriptions. Thanks to the narrative part, here the immersion can be important. I personally think that the uniques are very important and a very interesting feature of EBII.
-Governments & Colonies: They are similar to the uniques although more important due to they are the basis of the campaign. The more variety they offer, the more fun the campaign will be. Again, the Celtiberians will work as an example: during the early campaign the governments will allow you to develop several types of alliances/confederations with your neighbours (historicity). During the middle campaign you will be able to use your colonies that will be always the most interesting option: will you go to the east or to the west? will you go in the capacity of a group of raiders or as a group of mercenaries? will you establish a city-state in Lusitania or you prefer to make a pact with Greeks and Carthaginians in Sicily? Will you fight for them in order to obtain some farms in Sicily? (roleplay based on historical information).
Well, that is my humble opinion about the immersion in MTWII, being the traits and ancillaries the best option to increase it. Additionally EBII has governments, colonies and uniques that are also an amazing tool to get this immersion. As always, sorry for my potential grammar mistakes, although my English is not bad, it's not perfect at all.