First things First...
Logic does not read ADATsync as a viable sync source.
This would sound like a standard for any sequencer software and it is... but Logic won't have this until Version 5.0 so until then - the only SYNC sources you have are

INTERNAL MTC MIDI clock and MANUAL

Now in order for Logic to control your ADAT via MTC (Logic is the master setup)
you must have a dedicated Midi port on your interface that will be used to send MTC and MMC to the ADAT...

1) take the MIDI out of your (dedicated MIDI Port) into the MIDI IN of your ADAT
2) See your documentation depending on which ADAT you have, to determine how to set your ADAT for MMC control
3) launch logic
4) Go to the OPTIONS > SETTINGS > SYNCRONIZATION settings
there will 4 tabs there... GENERAL - AUDIO - MIDI - and UNITOR
5) Choose the MIDI tab
6) please check the boxes that says TRANSMIT MTC and TRANSMIT MMC
7) next to each of those boxes there should be a selection where you can choose which MIDIport you want to send MTC/MMC out of ... choose for both
8)go back to the GENERAL page
9) you must choose a frame rate (24,25,29.97 and so on)
10) Since this setup is for LOGIC being the MASTER, the SYNC MODE source stays at INTERNAL
11) and check the box by AUTO ENABLE EXTERNAL SYNC
12) Set your SMTPE offset in it's box (If needed)

now close this page and when you push the play button on your transport the ADAT should respond and move to wherever the location is on your song...