You're saying that the TC changes from DF to NDF right around the start of the transfer?
That kind of thing, an incorrectly striped tape, could mess up how FCP calculates the preroll and modify your capture start.
I would mess around with capturing exactly 10 sec chunks of tape from before, across, and after the TC switch and, if possible capturing with the Beta decks TC burnt in to the picture to see what's going on w.r.t. what FCP thinks it's getting.
ak
Sleeplings, AWAKE!