Lots of potential issues here. Firstly you have a DV sequence and a Blackmagic card. I assume you have selected the correct Blackmagic DV Easy Setup which gives you an SDI output from the card into the digi beta and RS422 machine control.
If so, can you see your Final Cut output looping through the digi beta deck? If yes, then do you have common reference video going to both the digi beta and the Decklink card? Next,is the digi beta setup to reference the input signal or the reference signal?
Finally is the assemble editing picking up during the timecoded pre black section. Also the timecode needs to be setup correctly although it sounds like you have problems back in the SDI and reference area. Lets solve them first.