If the transformer was not specified properly, a savvy (or sneaky) transformer supplier will take advantage of the situation by providing a lower KVA transformer, sticking fans on it, and getting anywhere from 115%, 125%, and on real large units 133% increase in power output. It is cheaper to buy less KVA, and put on fans, then to buy full KVA without fans. The way metal prices have skyrocketed that maybe what occured. If there were space limitations in the spec, this may be how they were able to shrink it down in size, but still get the needed KVA.
At 480V HV side, most likely the fan power is tapped from there as mentioned. Since you can continue to operate without the fans, especially at a lower KVA, I doubt the initial alarm will cause a shutdown. It may also have a high/high alarm setting that will need to be wired to trip the primary breaker. Check the warranty to see what happens when the fans crap out.