For the few years ive been using my TI with total integration only so I can remember if, when only using midi cables (old school setup) TI receives SPP (song position pointer I think) to keep the lfo's playing back correctly no matter where you put your start marker in your daw.
For example if I have a slow 8 bar lfo phase then the phase will stay static throught those 8 bars, regardless of changing the playback point in the song.
I actually would like to know about the C models ability or inability to do this as I plan on purchasing one to add to the small power of the TI snow.