Generally, you're considering that Class 1E circuit traces back to the buss that is supplied by your emergency diesels. In our plant, our Class 1E buss is 4160V. It is normally fed from offsite power, which is NOT Class 1E. But, in the event the offsite power feed is lost, the emergency diesel generator supplies the power to the Class 1E buss. All of the components associated with the EDG's are safety related, thus assuring that you can provide power to the Class 1E equipment. Your unit aux transformer is likely NOT safety related.
So, for example, our Class 1E buss is 4160V, which feeds some important pumps, etc. and several 480V load centers. Those load centers then feed multiple other components and some 480V/240V/120V transformers that feed to other components/circuit panels. All of this is considered Class 1E. We also have similar systems that are not considered Class 1 to feed circuits that do not have safety related equipment/components. The primary difference is that the non-Class 1E systems do not have the backup emergency power supplies. So, if we lose offsite power, the non-Class 1E circuit will not have power.