I think a part of his mouth bothered him and force him to touch it with his tongue. Someone made a comment months ago about Alexei teeth not being the best and he even had a gap between the two from incisives.
Is either that or he just had that habit. Still, the first time I saw that picture with his cheek swollen I thought he had some kind of candy and instead of carrying it in his hand he just store it between his teeth and cheek.