Yup while for Tumnus, he was around for a lot of things but I think he was young when the White Witch came to power and a lot of the people who faced her are gone.

So he's trying to put the pieces together along with keeping a record of how the Pevensies are ruling since he was right at the beginning.

I think a part of it is that he lost time when he was a statue and that still bothers him a lot so his natural historian tendencies are just a bit more.