This particular building is fed with 13kv. The 13kv terminates in a rotary puffer switch, which then feeds two transformers. One transformer steps the 13kv down to 208Y120v for one switchgear cabinet and the other transformer steps the 13kv down to 480Y277v for another switchgear cabinet. The transfer switch's normal power originates from the 208Y120v gear. The transfer switch's alternate source originates from the 480Y277v gear, but is first stepped down via a 480 delta primary 208Y120v secondary transformer. The only variable here seems to be the transformers. So, is it safe to say that the transformers are the culprits as far as the phase differential goes?
Well iam not a expert but you have both transformers online correct and there loaded .
One swbd on one and one swbd on the other the 30 deg phase shift is from primary to secondary internal inside each so i dont see it being a problem.
Your issue is there out of phase after secondary they dont match when you want the emergency power correct and voltage is off and phases dont match correct ?
Transfer phase monitor can be adjusted or bypassed to just test transfer if you want under no load you can do that just to see if transfer switch is working ok .
But this is my thinking if the other transformer is or has issues like overloading PF bad you may have a phase shift between each or the normal source is overloaded it maybe out of phase with the other our these loaded with motors or that kind of loads .
If not i would bypass the phase monitor and turn it on but dont do it with motor loads online .
The only other reason is bad connections in transformers both or one long distance between each meaning power lines feeding transformers .
Last solution would be and your not going to do this but they make a PST transformer which will change phase shift from input to output power companys use these when they have long lines and impedance & capacitance problems on long parallel transmission .
Other than that voltage is a +/_ a few volts does not mean your out of phase just maybe a differance between windings of each and loads on them .
Dont use a meter connect a lite bulb up between a/a b/b/ c/c/ of opposite sources do they work if not its just the meter picking up voltage .
Your scope used on each can pick up capacitance between connection and be off you may not be so far off lastly i think its your transfer switch just getting old or that old puffer switch.