The shop I left in 2011 had zeta 3s for layback to video decks from pro tools . You do need sync I/O to make the zeta lock tape to protools master. If as mentioned , you lock protools to master multitrack, then all you need is a digi sync I/o and do not need the zeta. We had 5 to 6 zeta 3’s and only one of them worked correctly at the end of my tenure. You might be fighting multiple problems. The manual is confusing along with the menus on the zeta. Do you know the zeta is working correctly?
Besides the recording I spent a lot of hours keeping thing operating correctly that I did not get paid for. Mostly keeping the 24track running correctly.