balanced to the DA78, unbalanced RCA to the TSR. You will notice a difference in output levels o the TSR as it's output level is -10dBV and the DA78 is +4DBu.
As far as sync. if the DA78 outputs SMPTE, thread up some tape and stripe (record) the smpte signal onto an outer track, leave the adjacent track as a buffer (this is important because if you record say drums on the adjacent track, some of the peaks will modulate the time code and all will be lost.)
Once the tape is striped. Connect track 8 (or whatever the stripe is on) to smpte input on the DA78, put it into Timecode Chase mode and run the tape machine as the master.