I think that is correct for overload, but the listed fire pump controller will have short-circuit protection:
695.6 (C) Overload Protection.
Power circuits shall not have automatic protection against overloads. Except for protection of transformer primaries provided in
695.5(C)(2), branch-circuit and feeder conductors shall be protected against short circuit only. Where a tap is made to supply a fire pump, the wiring shall be treated as service conductors in accordance with
230.6. The applicable distance and size restrictions in
240.21 shall not apply.
If you're sizing the transformer you'll need to take into account 695.7 for Voltage Drop:
(A) Starting.
The voltage at the fire pump controller line terminals shall not drop more than 15 percent below normal (controller-rated voltage) under motor starting conditions.
Exception: This limitation shall not apply for emergency run mechanical starting. [
20:9.4.2]
(B) Running.
The voltage at the load terminals of the fire pump controller shall not drop more than 5 percent below the voltage rating of the motor connected to those terminals when the motor is operating at 115 percent of the full-load current rating of the motor.
I've done this in the past and used the Utility's MV source contribution along with the transformer impedance and X/R ratio for the calculation.