I hate to say THIS (actually, no I don't
)
but in cases where the anime and manga conflict, IMHO the manga is canon. It's where the creator has the most control, sometimes the anime is edited
by someone else in order to make the story flow better according to
their standards, not the creator's.
That said, the manga gives a very strong impression (not explicitly stated, but heavily implied) that the Kaiten has been in Neji's arsenal for quite a while. As Tenten describes the move, nowhere does she say it's a recent addition, recently mastered, or anything to indicate that Neji learned it within the month.
Remember, the Ura Renge has a time limit. If Neji can somehow, in some secret way fend off Rock for the time period (seems to be less than 5 minutes?) then Rock will be completely, utterly defenseless.